Style advice on how to punctuate a numerical range intersects with style advice on whether to spell out numbers or use numerals. To keep the coverage here shorter than it otherwise would be, however, I will focus on what style guides say about punctuating number ranges, without regard to whether they recommend spelling out the numbers or rendering them as numerals on account of their magnitude. I consulted a number of style guides (mostly concerned with U.S. style) to see what advice they might offer on how to handle inclusive number ranges. Here is what I found.
U.S. and British book style
From The Chicago Manual of Style, sixteenth edition (2010):
Inclusive Numbers
9.58 When to use the en dash. An en dash used between two numbers implies up to and including, or through. ... [Examples:]
Please refer to pages 75–110.
Here are the figures for 2001–10.
Campers were divided into age groups 5–7, 8–10, 11–13, and 14–16.
9.59 When not to use the en dash. If from or between is used before the first of a pair of numbers, the en dash should not be used; instead from should be followed by to or through, between should be followed by and. [Examples:]
from 75 to 110 (not from 75–110)
from 1898 to 1903
from January 1, 1898, through December 31, 1903
between about 150 and 200
In the preceding guidelines, Chicago never mentions the possibility of using hyphens or em dashes in inclusive numerical ranges. That's because Chicago views the en dash as the only correct dash mark to use in instances involving inclusive numbers. According to Chicago, hyphens, when used with numbers, function not as connectors but as separators:
6.77 Hyphens as separators. A hyphen is used to separate numbers that are not inclusive, such as telephone numbers, social security numbers, and ISBNs. ...
And em dashes, according to Chicago (at 6.82), have no particular application to numbers at all:
Em dashes are used to set off an amplifying or explanatory element and in that sense can function as an alternative to parentheses, commas, or a colon—especially when an abrupt break in thought is called for.
In contrast, Chicago says (at 6.78), "The principle use of the en dash is to connect numbers and, less often, words." Chicago doesn't explicitly address the question of whether to leave letter spaces around an en dash or to close up the terms on either side of it, but every example it provides that includes an en dash shows the en dash closed up. It follows that, of the seven possibilities cited in the question above, Chicago would endorse only #1 and #5.
Merriam-Webster's Webster's Standard American Style Manual (1985) closely aligns with Chicago on the handling of inclusive number ranges:
Inclusive Numbers
11. Inclusive numbers—those which express a range—are separated by either the word to or by an en dash, which serves as an arbitrary equivalent of the phrase (up) to and including" when used between dates and other inclusive numbers. ... [Examples:]
pages 40 to 98 | pages 40–98 | pp. 40–98 | 14–18 months | the years 1960–1965 | spanning the years 1915 to 1941 | the decade 1920–1930 | the fiscal year 1984–1985
NOTE: Inclusive numbers separated by an en dash are not used in combination with the words from or between, as in "from 1950–60" or "between 1970–90." Instead, phrases like these are written as "from 1955 to 1960" and "between 1970 and 1990."
Again, options #1 and #5 are the only ones that the guide endorses.
Words into Type, third edition (1974) is likewise on board with most of Chicago's guidelines:
Inclusive page numbers may be given in full ("413–415") or elided ("413–15"); either way, when type is set an en dash, not a hyphen, should be used.
...
Elision. If two year numbers are connected, the hundreds may be omitted from the second unless the first number in two ciphers [that is, zeroes], when the full number must be repeated. In some styles, only one numeral is needed after the dash. [Examples:]
1775–79 | 1800–1801 | 1901–2 | 1453–7
The same principle may apply to inclusive page number, especially in indexes. [Examples:]
8–10, 22–23, 100–103, 119–22, 1074–76
In such elisions an en dash should be used; never use an en dash when the numbers are preceded by from or between. [Examples:]
from 1892 to 1898 | between 1955 and 1960
Here, too, the only approved options are #1 and #5.
Although The Oxford Guide to Style (2002) calls the punctuation mark an en rule rather than an en dash, it prescribes essentially the same rules for using the mark:
Use the en rule closed up (non-touching) to denote elision in element that form a range:
pp. 23–36 | pp. x-–xvii | 1939–45 | Monday–Saturday | Tues.–Thurs. | 9.30–5.30
Note that it is the 1939–45 war but the war from 1939 to 1945.
In short, Oxford, like Chicago and its other U.S. counterparts, endorses options #1 and #5.
U.S. newspaper style
In discussing square brackets ([]), The Associated Press Stylebook (2007) has this interesting note:
brackets [ ] They cannot be transmitted over news wires. Use parentheses or recast the material.
Some similar past or present constraint seems to have inclined AP to avoid the use of en dashes under virtually any circumstance. The Stylebook offers the following relevant examples where a closed-up hyphen takes the place of the word to:
a 5-4 court decision | a ratio of 2-to-1 [or] a 2-1 ratio | a 4-3 score
In general AP seems to favor avoiding sentences with inclusive numerical ranges, as it offers no advice on how to punctuate date ranges, page ranges, or other common ranges. In instances involving a range of percentages or of money estimates, AP recommends spelling out the word to rather than using a hyphen or a dash:
a pay increase of 12 percent to 15 percent. Or: a pay increase of between 12 percent and 15 percent
Also: from $12 million to $14 million
From these examples, it appears that AP would approve of option #1 and (in a pinch) option #3 of the options posted in the question above.
Unlike AP, The New York Times Manual of Style and Usage (1999) explicitly forbids use of the en dash for most purposes:
The dash used in news copy is one em wide. Do not use the shorter en dash (–), except as a minus sign.
It follows that the New York Times favors using hyphens rather than en dashes to mark numerical ranges in cases where spelling out to is inconvenient or awkward—and indeed the Manual provides at least a couple of examples where this is the case:
page numbers. Capitalize them as proper names: Page A1; Page A14; Page B1; Page 112; Pages A18-20. ... In charts, diagrams and tables, abbreviations may be used: P. 5; Pp. 19, 20 and 21; Pp. 19-21.
In these examples, "Pp. A18-20" would have been rendered as either "pages [or pp.] A18–A20" or "pages [or pp.] A18–20" (with an en dash rather than a hyphen as the connective punctuation) in any of the book style guides discussed in the previous section of this answer; and likewise "Pp. 19-21" would have been rendered as "pages [or pp.] 19–21" (again with an en dash rather than a hyphen).
Likewise, in its entry for years, decades, centuries, The New York Times Manual of Style and Usage recommends using a hyphen as the linking punctuation mark:
Give the spans of years this way: 1861-65; 1880-95; 1895-1900; 1903-4 (not 1903-04).
By and large, however, the New York Times seems inclined to follow AP in preferring to spell out numerical ranges rather than linking them with punctuation marks. It thus appears that options #1 and #3 are acceptable to this style guide.
Kenneth Wilson, The Columbia Guide to Standard American English (1997) seems to assume that readers will not have access to machines capable of producing en dashes:
To show dates from and to, use either a hyphen (printing uses something called an en dash, a mark about twice as long as a hyphen and half the size of an em dash)—June–October, 1978; January 1–15, 1990—or the prepositions.
The odd thing here is that after telling readers to use a hyphen for date ranges, Wilson gives two examples that use en dashes rather than hyphens. Perhaps this is simply evidence that, as he says, "printing uses something called an en dash" for this purpose"—but I suspect that some proofreader or copy editor "corrected" the hyphens by replacing them with en dashes, contrary to Wilson's intention in this case. Again options #1 and #3 are favored here—at least for people not working in "printing").
Conclusions
The primary split in preferences regarding how to represent numerical ranges that appeared in the style guides that I consulted was not between British punctuation style and U.S. punctuation style (Oxford and Chicago closely agree on the main points of such style) nor between styles favoring open punctuation (letter spaces on either side of the punctuation mark) versus closed punctuation (no letter space on either side of the mark)—I couldn't find any style guide that endorsed the open style for inclusive numbers.
Rather it was between using an en dash as the linking punctuation (favored by most book publishers) and using a hyphen for this purpose (favored by most newspaper styles).
With reference to the seven options proposed in the posted question, option #1 ("Use the word 'to' as in '10 to 20'.") earns support—albeit not exclusive support—across the board; option #3 ("Use a hyphen not separated by spaces as in '10-20'.") wins the approval of newspaper publishers and of one guide that seems directed toward people who don't have ready access to en dashes; and option #5 ("Use an en dash not separated by spaces, as in '10–20'.") is vigorously championed by book publishers. The remaining options receive no visible support at all.
EN DASHnot aHYPHEN-MINUSfor ranges, per many, many style guides including Chicago.