Upvote:2
You haven't provided sufficient information for a detailed response. If you're booked on a single ticket or several with airlines that have agreements, and the route is a series of layovers, it will affect how your luggage is handled. If these are four separate tickets on four different airlines, you would have to collect and recheck your bags at each stop.
Here's a general idea of what you might experience:
Guam: the territory has its own customs process, and it's quick and easy. After that, you go US Customs and Immigration pre-clearance.
Honolulu: you'll go through US Department of Agriculture inspection (but not Customs or Immigration as you've been pre-cleared in Guam).
Los Angeles: this is a domestic arrival and you'll go from your arrival gate to the departure gate for your onward flight to New Mexico.
Albuquerque: collect your bags and leave the airport.