Ms. Cindy,
If you catch your crow, you should see if he'll let you tag him. Try putting a lil cuff around his foot. You can take him to the vet to do this if you want i believe. but ya, Ravins and crows are one of the smartest birds out there ^.^ They could talk if they had the proper structure
Is there any chance that you could walk or ride a bike from your house to your new house? Cuz if you did that, and then just stayed at ur new house, i'm pretty sure he'd get the idea pretty easily that that's ur new location. Just make sure he's following you somehow ^.^ That might be hard though, cuz they can be pretty stelthy when they wana follow someone.
*thinks* don't worry about transporting Lola either. If its just a car ride across town like you say, then you can just take her in a box. The box keeps her blinded from what's outside so she won't get stressed out, and she'll just come out in a new place and be like "huh?" for a while. But she'll get used to it in less than a day
~Phoebe