Under the sinks you will see a valve like above. Its purpose is to let air IN the line when the tank is draining, so the P traps do not get sucked dry. It is not supposed to let air out. Sounds like yours are letting air out and need replacing. They just screw in to the drain and are not hard to change.
The other thing you have is a roof vent for the gray and black tanks. It is just to equalize pressure. If that vent is plugged up, the gray tank could be burping back through the trap. They get plugged up with insect or birds nests. Also the vent pipe can slide down and be sitting on the bottom of the tank. Someone needs to climb on top of the trailer and check out that vent pipe.
Check the above items. Then dump the gray tank, fill it and dump repeatedly.
Many people add a combination of borax and dish soap to the tank and drive around with it about 3/4 full for a while. Then fill it up all the way and dump it.
Do the above and see if that doesn't help.