Not getting any audio with some of these (just in the Hungarian course), including this one sentence. Just me?
This is the imperative, telling someone to go there.
If you are asking about the word order, ie. "oda menj" vs. "menj oda", that is a matter of emphasis. A simple "go there" is "menj oda". But if someone is going to the wrong place, then you would tell them:
"No, do not go there, go over there instead!" That would be "Oda menj", not to some other place.
I am going there - Odamegyek. It's not an imperative sentence, unlike 'oda menj!'
It does sound similar to "meny", even more to "menny" with long ny, actually. I'm not sure about the terminology but the general rule is you don't make stops between consonants next to each other so all kind of assimilations come into play, just like here, n and j merging into a (long) ny