Would

whatchadoinDoes this sentence sound awkward?

Not to me. Better, I think, is I would like it if you came with me.

It's fine, in my opinion. The condition is about the willingness on his part to come with you. Note that it's different from Gus's example , in that that his sentence suggests that you think he's probably not going to come with you (though admittedly it could just be a polite request).

It sounds more like an invitation to me:

I'm going to the store. I would like it if you came with me.
˜ I'm going to the store. Would you like to come with me?

The second conditional is usually used for unreal or highly improbable situations, although native speakers don't always use the construction for that purpose, and this, I would say, is such a case

Aspara GusIt sounds more like an invitation to me

And I don't object to that. Still, "would come" (in an if-clause) often suggests willingness to do something.