"Will you come too?" is "Vil du være med du også?". This sounds more like you're asking a person to join the group and do something. "Vil du bli med?" is kind of the same, but it isn't as implied that it is a group that is asking, as in "Vil du være med du også?". That sounds more like a person standing alone and then a group of friends asks the person if he/she wants to come along.
I think you use 'vil ha' when you want to have something, for eksempel, 'jeg vil ha iskrem' = 'I want (to have) ice cream'. But you can't use 'vil ha' when saying 'I want to come along', because it wouldn't make sense; the verb 'to have' doesn't appear in the sentence. So you just use 'vil', not 'vil ha' - 'jeg vil bli med' = 'I want to come along'. I'm not an expert at all, so maybe a native could confirm this? :)