I find myself using phrases like "[such and such] saw an increase on last year" or "we are up on last year"
I would be inclined to use just "since last year", but that doesn't really work if comparing a specific month from last year to the same month this year.
Are these standard usage?
With regard to usage I would say that it's somewhat commonly used, specifically in (news) reports: https://www.google.com/search?q=%22saw+an+increase+on+last+year%22.
With regard to grammar I imagine that it's a slightly abbreviated form of something along the lines of: "This year's harvest saw an increase of 5% on top of last year's harvest". There's last year's harvest and the increase is 'on top of' that of last year, which is probably why the 'on' preposition works. At least, I feel like it is. If you put it in a more conversational sense, you'd get: "I put in 3 potatoes on what I usually do". It's the same type of structure, but you clearly need 'on top of' here. It's not extremely thorough, nor backed up by any grammar book, but it feels to me like the "saw an increase on last year" structure is an abbreviated phrase used solely for that type of reportage.
But I get why you'd be more inclined towards other ways of phrasing it, but I'd avoid 'since', which indeed indicates that the entire period between point A and point B was required to reach a certain increase ("Since last month I've collected three rocks!"), as opposed to comparing two points in time (Compared to what I got last month, I collected three more rocks!").
My personal preference would go for something like "Compared to last year, this year's harvest had an increase of 5%", but that's likely because I don't do much in the way of reporting for longitudinal studies or projects.
It is one thing to use a phrase in speech and another to write it out. In speaking, the context and cues probably help qualify what you mean precisely.
For writing, I would agree with your suggestion of "Our revenue has increased since last year" or "Our total orders have increased from 1.5MM units to 2.2MM units." The alternatives to these examples read poorly: "Our revenue has increased on last year" or "Our total orders have increased on 1.5MM units to 2.2MM units."
Now, the phrase "to be up on" has a stronger grammatical argument, since you would be up on something, e.g., "Place the book up on the counter," or "Our currents numbers are up on last year's"
'Since' relates to the time period.
'On' relates to the comparison or increase.
You would use 'since' if you wish to put more focus on the time period, and you would use 'on' to focus on the increase.
It is also possible to use 'over' in a similar manner to 'on' although it would need the clarification of 'increase'.
[such and such] saw an increase over last year
or the negative 'decrease'
[such and such] saw a decrease over last year
Unless this is a very casual sort of comparison, I would use year-over-year (frequently seen without the hyphens).
: comparing or based on comparing the same time period in successive years year-over-year growth year-over-year increases/declines
"Year-over-year." Merriam-Webster.com. Merriam-Webster, n.d. Web. 28 June 2018.
So your sentence would become "we saw a year-over-year increase in [such and such] of X amount". This works fine in any register from formal and technical to casual. Although saw is limited to you actually experiencing something as an observer, otherwise you need to replace it with a different verb.
The short answer is that I have never seen or heard on used that way and I find it non-idiomatic.
I haven't found a relevant example in the dictionaries I've checked (CED, M-W), but here is a typical example from the Daily Mirror:
20 Apr 2018 – It saw the National Living Wage rise from £7.50 to £7.83 an hour – a 4.7% increase on last year.
There is obviously a deletion, from ' ... on last year's figure' / 'on the NLW as it was last year' ....
'We are up on last year' could be seen as an example of metonymy ('we' for 'our profits'), but is probably better just seen as another shortened form (not that there's much difference here).
