This is what I am looking for: a travel case for my PSP that holds the
PSP, at least 6-8 UMDs (or maybe I could just throw my airform case in
there), the charger, car charger, earbuds, etc. ALSO, I have the
Logitech PlayGear Pocket, and I want the PSP inside the Logitech case
to fit inside the travel case. I don't want to take the PSP out of the
awesome Logitech case and put it inside another case for traveling.

Here is the Logitech case:
http://www.logitech.com/index.cfm/products/details/US/EN,CRID=2362,CONTENTID=10181

And the Airform pouches: http://shop.brando.com.hk/airformumdpouch.php

I haven't found a suitable case that holds everything. Please help!

This could be the solution:

http://www.inteclink.com/inteclink/products/psp/psp.asp#6783

I have looked at these but you can only snugly fit the PSP, not the
PSP inside the Logitech case.

Well, the first thing that comes to mind while looking at this
question? really look at camera bags? actually that was the second
thing, the first was that a dry box might end up being exactly what
you are looking for.

Those who Scuba Dive know the difficulty of protecting any sort of
electronics on a boat where they are likely to get soaked. and there
are a vast variety of cases available to counteract the submersion
under water and really any other abuse that is thrown at the cases
available. From personal experience I recommend Pelican Cases.
http://www.pelican.com/cases/cases.html
while I am not certain of the size the Game boy color case may fit
everything you need, you can find it in the micro category or else
simply one of the small cases. The cases come filled with the foam you
see, and are easy to cut to exact dimensions with a razor blade, so
you could easily cut slots for your PSP and related accessories. Not
only that, the cases are completely water proof, most to 300 meters..
one cannot say that about the opposition.

Before you rule me out as a fool, go to a diving store and look at the
cases available. They may well work, and many manufactures will
include a warrantee on both the case and the contents against
destruction of any kind.

Other brands and or things you may consider size dependent
http://www.otterbox.com/index.htm (may be too small, unsure..)
http://www.uwkinetics.com/CategoryDisplay_cgmenbr=91&cgrfnbr=837.htm

I do realize that the molded composite is not to everyone?s liking,
and may well be a deciding factor against buying such a case. Apart
from the above mentioned I would advise trying someplace such as
http://www.ebags.com/ for a hard case, or if you do not mind a soft
case then any luggage store, from personal experience I recommend
Coach. However if they are out of the budget then any luggage store
should sell the sort of bag you are looking for