I have the quest "ED-E My Love". However, I cannot just pick him up and walk outside (he's in a house). Is it possible to do that quest when I don't have the science/repair to fix him first?
No. You'll need to get Ed-E fixed up first. If you lack the requisite Science or Repair skills, you should be able to substitute a lot of parts for any actual knowledge. Specifically, 3 Scrap Metal, 2 Sensor Modules, and one Scrap Electronics.
Alternately, you can just come back later, or pop a Skill Magazine.