Cockroaches love moisture, so concentrate treatment in the kitchen and bathroom. Diatomaceous earth can be sprinkled around in cabinets. It is harmless to humans and pets. On roaches... it's like eating glass and destroys their exoskeletons. May take up to 2 weeks to work. Catnip is a natural repellant and can be brewed and used as a spray. The eggs are encased in an eggsack, about the size of a partially engorged tick. They can drop the sack anywhere.
When packing, shake out any clothing if your apartment is heavily infested. You can sprinkle Diatomaceous earth in the bottoms of any boxes, and cache's of catnip in with anything.
Glue traps Warning: I came home from work one day to hear a swoosh-swoosh sound coming from my apartment. I was afraid to enter. When I did, I found my Yorkie with one glue trap stuck on each front foot, and glue all over his mouth where he had tried to chew the traps off. I spend the next four hours trying to find something that would cut the adhesive. The last thing I tried was GoJo Orange hand cleaner (for mechanics) This cut the adhesive quite easily, and I followed that immediately with Dawn dishwashing liquid, to make sure all the hand cleaner was gone.
Natural Insect Pest Control - Eartheasy.com Solutions for Sustainable Living