word choice - "Feel free to hit me up" — "at"? "on"? "via"?

As others have noted, "hit me up" is not normally understood to mean "contact me". In the context, where you are immediately following it with an email address, it's pretty clear what you mean. But if you just said to someone, "Hey, hit me up later", I think they'd be unsure what you meant. As GEdgar says, in English "hit me up" is an old slang term for "borrow money from me".

That said, "at" is used to indicate that what follows is a location. "I am at home." "We met at the hardware store."

"On" is used to indicate attached to or resting atop what follows. What follows "on" is usually an object, like "on the table", but it could be a location when we think of the location as something you stand upon, like "on the beach" or "on a road".

"Via" means that what follows is a route or way-point. "We traveled from France to Germany via Switzerland."

So we normally say "at" when giving an address. This applies whether it's a street address, phone number, email address, and any other sort of address I can think of. "You can contact me at guy@example.com", "Call me at 734-555-1111", "The store is at 23 Elm St", etc.

We say something is "on" a Website. "I am on Facebook". Personally I don't think it makes sense to say "You can contact me on/at Facebook", because we don't really "contact" people with Facebook. You might "Visit my page on Facebook" or "Leave a message for me on Facebook". I think either "on" or "at" would work for messages on a website, because we think of a website as both a place where things can be "at", and as a surface that things can be "on". Like you could say, "Leave a note at my house", but you wouldn't normally say "Leave a note on my house" unless you meant that they should write it on the walls. But we do say "Leave a note on the bulletin board."

I wouldn't use "via" for an address. I suppose you could say that the message is travelling through your email account to get to you, so it's going "via my email address". But I've never heard someone say that. It's not necessarily wrong, but it's odd.