Sounds like a blocked tank vent
Any gurgling sound or "burping" after pumping in either mode is a strong indication that the tank vent IS blocked, but don't assume that no burp or gurgling means the vent isn't blocked. When the vent becomes blocked, air in the tank that's displaced by incoming waste has nowhere to go, so the system becomes pressurized, creating back pressure that sends flushes back to the bowl. If the system become pressurized enough, it won't just "burp," it can erupt! It can also result in burst tank. A blocked vent will also cause a pumpout or macerator to pull a vacuum that prevents anything from being pulled out.
Problems caused by tank vent blockages are very common in the spring because spring is when dirt daubers are building their mud nests in every opening they can find, and they LOVE vent thru-hulls. So first thing to check is the vent thru-hull...scrape out what you find with a screwdriver or whatever works. The other most common place for a vent blockage is the other end of the vent line--the vent fitting on the tank AND that end of the vent line. Remove it...scrape it out.
Joker valves should be replaced annually as preventive maintenance, so if you haven't done that in at least a year do it. However, I wouldn't put ANY money into rebuild kit for a Jabsco toilet...you can buy the whole pump for only about 20% more. If the toilet needs more than a joker valve, upgrade to a PHC
sbo.com PHII PHC LBA
And if there's no vented loop in the toilet intake, install one. Without it, the boat can sink in its slip if the toilet is accidentally left in the wet mode when you leave it. See the drawing in the instructions for the correct location (between the pump and the bowl, NOT in the line between the thru-hull and the pump):
Jabsco manual toilet instructions
Luz, I suspect your odor problem is due to more than one problem. Odor in the toilet is most likely to be stagnant sea water or dead decaying animal vegetable sea life trapped in the head intake. Fill a bucket with clean fresh water to which you've added a quart of WHITE vinegar...disconnect the head intake line from the thru-hull (close the seacock first)...stick in the bucket and pump the whole bucketful through to the tank.
Odor out the vent is from the tank. What tank product are you using? Flush it out again, this time putting the water into the tank via deck pumpout fitting...cuz that sends the water into the tank at the bottom to stir up any sludge so it can be pumped out. You only need a few inches of water in the tank...so add water, pump that out...add water, pump it out...till you're only pumping clean water. Then, if you have a macerator pump, do it one more time, but instead of pumping it out, turn on the macerator to rinse out that plumbing.
You also need to check and clean out the tank vent (remove any filter in the vent line) and replace the joker valve.
and then a month or so ago, it was evidently full, we could not use pump out due to some issues related to the Tsunami so I had the service come around and pump out for us while we were away during the next week. Ever since, we have had an odor that comes from the toilet until I flush and clean upon boarding the boat after a week, and even then I still think I smell something! Also there is now a smell at the vent when pumping and in general I am not as proud of my normally wonderfully clean and great smelling head!! BTW, the week after having the service pump the HT, we went to the pump out and did it again, flushing water through the system probably 4 times.
