[Didn't realise you meant how it sounded, read edit instead.] Gramatically, number three is correct in my opinion. Number two has a spelling mistake (Unless this is not intentional, if it isn't, three still sounds correct). One and two both have a semi-colon ( ; ). I think that would be incorrect grammar without a second sentence following the semi-colon. Considering it is a single statement, the third one must be correct.
EDIT: In terms of "into", "in on" and "in our", I believe "into our" would be more appropriate.
I like 1 (with correction of ; as noted) and 3a He kept butting in to our conversation. (The space/pause makes a difference.) The phrasal verb is "butting in" - (butting in) (to our conversation) not (butting) (into our conversation). He wasn't butting - he was butting in.