Could you tell me the difference between come in and come on in?

There is no difference in meaning. I think "come in" is the most common. "Come on in" may be used more often if the people have been talking outside. It is slightly more relaxed and friendly.

Alternative ways of saying the same thing are "come inside" and "step inside"

I hope this helps.

......................

"Come in!" is more formal than "Come on in!", and doesn't have the same degree of enthusiasm and pleasure.

"Come in" is what I'd say to somebody I didn't know or like. "Come on in!" is what I'd say to somebody I really cared about, like a close friend or family member.

https://forum.wordreference.com/threads/come-in-come-on-in.320877/