Well, Fowler's
Modern English Usage is strangely silent on this point!

I would say geeky is more common ("Owning 3 original console arcade games of Space Invaders is very geeky"), but I like the somewhat archaic sound of "geekly," so I would use that too, although sparingly. Maybe to describe activities meant to be portrayed as typical of geeks. ("Tony geekly dressed up as his favorite anime character before attending the con.")