No, it would sound very silly (to Hungarians)

No, it is not correct because of the word order.

yes

Well I'm glad that's settled

It's not a sentence. "Oda megyek" (I go there) or "oda megy" (he/she goes there) would be a sentence. In these sentences (and in the phrase "oda menni”), "oda” refers to a concrete place, e.g. 1. You are pointing at a place while you are saying "oda megyek.” 2. You mentioned the place in the conversation before. (Have you been to Hungary? I'll go there. – Voltál Magyarországon? Oda megyek.) (The tenses are completely different in the Hungarian language. We often use present form, when we are talking about the future. It isn't slang, it's grammatically correct.) 3. In complex sentences, like "I am going (there) where I was yesterday." – "Oda megyek, ahol tegnap voltam.” Don’t mix up with „odamegy”. It means „go”, but it refers to the fact that the activity has a goal and an ending. The verb „megy” refers only to the activity.

It means "there", but unlike "ott" it is used when talking about moving to a place.

Oda megyünk.
or
Mi oda megyünk.