As far as I know, this one is a tricky one: "venite!" is for the 2nd plural imperative: (You all) come! 2nd singular would be: "Vieni!" "Come!"
"Venga!" is however 3rd person singular ("he shall come!") which is used in this context as a formal you: "(Sir,) Come!
I'm sure it is explained in more details elsewhere, but here it might be enough. It also make senses to examine a bit full conjugation tables (Imperative column) to understand better. You will find a good one here: http://www.italian-verbs.com/italian-verbs/conjugation.php?verbo=venire
Venga is in the subjunctive, used for polite requests. I think it's confusing to toss it in here with all the informal stuff (like 'dimmi') if there's nothing in the sentence to give you a clue about context. Anyway - it's a formal way of ordering someone about. :)
I've seen "venga" used to mean "come" but also "venite"...what is it that distinguishes the italian infinitive?
I believe "venga" is the singular imperative while "venite" is the plural.
Your question is a bit unclear, but as SamMWBlake has answered parts of it, I'll try to answer the rest.
The Italian infitives I've seen so far end in either -ere, -are or -ire. You may also find infinitives being used as negative imperatives, e.g. "Non venire qua!" ("Do not come here!").