What is Yoda's speech called? Is there a particular name for it (such as "dangling...")?
This is more a linguistics question than an English language question in my opinion.
The quality of Yoda's speech that makes it sound strange to English speakers - and the speakers of the majority of earth's langauges is that it uses a very uncommon linguistic typology or word ordering known as Object-Subject-Verb (OSV) or sometimes Object-Agent-Verb (OAV).
One way to look at Yoda's syntax is that it shows signs of favoring OSV syntax (Object-Subject-Verb) as the basic order in the simple clause. In fact one could call it XSV syntax, where the X is whatever complement would appropriately go with the verb, whether it's an object or not.
But there is another way to see Yoda's syntax: you could see him as using SVO (or SVX) but favoring, almost to excess, certain special constructions that English allows only as stylistic variations in special discourse contexts.
Just saw a question about the topic not too long ago ;P
Hyperbaton: An inversion of normal word order. A generic term for a variety of figures involving transposition (see below), it is sometimes synonymous with anastrophe.
Anastrophe: Usually synonymous and occasionally referred to as a more specific instance of hyperbaton: the changing of the position of only a single word.
This style is found in certain forms of poetry. One example of Yoda's speech, "Sorry, but go you must." instead of "Sorry, but you must go." is seen attached to this small article.
A figure of speech that uses disruption or inversion of customary word order to produce a distinctive effect also, a figure in which language takes a sudden turn--usually an interruption.
Plural: hyperbata. Adjective: hyperbatonic....From the Greek, "passed over, transposed"
Here's a small example calling on the same phrase in a technical analogy from the University of Baltimore
Jay Bolter once showed me an interesting approach to the dialectic of singular and multiple sequences in hypertext (1992). He invoked the rhetorical figure of hyperbaton or scrambled syntax -- the way Yoda speaks in the Star Wars movies...
...in much the same way that we understand what Yoda means when he says, "Sorry I be but go you must." We register the disorder in the text but make sense of it by extrapolating a more conventional pattern.
here's a fairly thorough discussion of Yodish
Yodish, the language of Yoda of Star Wars fame is quite similar to that of our standard English. The words he uses are the same as those we use. They are intended to be used for the same purpose or part of speech. His language contains the same phrase structures and if enough applications are made, it is likely that infinite combinations are possible. Yodish is not an arbitrary grammar which simply confuses that of SEV willy-nilly but there is a standard pattern of rules which are applied, though not likely purposefully designed by creator George Lucas. If this were the case, the errors I have mentioned would very likely not exist nor would the fourth class of sentences, that of the SEV structures used for clarity of understanding. There are some exceptions to these rules, but we can apply the rules of Yodish and create an everyday language and therefore, Yodish is a legitimate language, or in the grammar of Yoda, "A legitimate language is Yodish, yes. Hmmm."