FLCL, Kemeko Deluxe! Recommendations
It's got the obvious elements, such as "boy meets alien girl", but it also has other similarities such as the wacky robot designs, the boy has a strange power in his head, and it's fast and crazy pacing, as well as having some hilarious moments. There are some obvious parallels between the two.
The shows are both insane crazy funny. Oh and of course there's the whole girl crashes into the life of boy and changes it forever, thing.
girl invades male's house, tries to make a relationship with him