How can I move my AOL contacts to either my GOOGLE contacts or my Motorola Droid X?
Specifically for moving your AOL contacts to your Google account, this page explains how to do that for a number of different E-mail providers. Unfortunately this is their answer for AOL:
AOL: AOL doesn't have the functionality to export your address book, so you'll have to create a custom CSV file if you use this service.
So it looks like you're stuck typing them all out manually if you want to move them to your Google account. I don't have a Droid X so I can't dig around in the settings, but I wouldn't be surprised if you didn't have any automatic options with that method either.
On the plus side you could use this as an opportunity to pare down your contact list. I do this every few months anyway, just to keep the people I actually need up to date and quickly available.
Edit: But wait! I just found this page which explains a clever way around AOL's lack of export functionality. It's a little weird, and could be considered inconvenient for everyone you want to move over, but at least it would keep you from having to type out all of your friends' and family's E-mail addresses. It relies on the fact that Gmail will auto-add anyone who you send an E-mail.
Edit 2: And yet another solution! This page explains a way to create a .csv file containing just E-mail addresses that you can import into Gmail without having to E-mail everyone twice.