Need help with using Testors Modelmaster Acryl paints...

Its not very great paint to begin with. But thats just my experience. I had better luck making my own thinner using a 50/50 mix with 70% rubbing alcohol and a flow aid mixed in.

I used to have trouble with MM Acryl but I didn't realize I had to keep the tip clean while spraying.  Make sure you stir them up really well (I use the Tamiya Stirrer) and use the MM Acryl thinner, you might also want to add a drop of Liquitex Flow Aid as well so they don't clog the needle tip as much.  

If the paint is runny its either not mixed up, your spraying too close or using too high a PSI.  Try adjusting it to about 15-20 PSI range and see if that helps.

plan your paint day then a few days before carry the bottle in your pocket for a couple days, warming it up slowly and the movement of your body helps mix the pigment with the carrier, also try dropping a couple of BB's  in the jar then shake and mix for about 30min .same idea as the marble in a rattle can

I find I don't have the control with acrylics that I have with enamels in my AB. For me, enamels spraying smoother and finer lines are not a problem at all. Acrylics tend to dry faster, causing the AB tip to act funny. If I have to AB acrylics, I use some retarder to slow down the drying time along with some flow improver. As previously mentioned, thinning with Future improves how it sprays out.

Silly question, maybe, but have you mixed/stirred them with a stick, not just shaking them?

Try adding a few drops of Future into the mix. It helps the stuff adhere a bit better and flow btter throw the airbrush.

I use MM Acrylics and never had a problem airbrushing. Try opening the nozzle tip. Sometimes I find myself forgetting to open up the nozzle tip when nothing comes out. How about the needle? Is it clean?

Yes, how old is OLD?  

I  just spent some time with a couple colors. They continue to work fine, even with minimal thinning.

I'm working on a project that is using Interior Black, Medium Green, Military Brown and Green Drab, none of which is fresh from the LHS.  I honestly don't recall when I bought them, but they have to be at least a year old. If they do need thinning, I use distilled water.

Is it possible you're thinning too much? Is your compressor pressure is too high? Is your airbrush tip too close for the pressure?  

When you say Older Testor Model Master Acryl paints,,,,,,,,do you mean the bottles with the Gray caps?