I have a very small 720 sq ft ranch house with what appears to be recently installed pvc piping. Now the problem, the plumbing gurgles and siphons or backs up into the tub. Not pretty. The warranty company has come out and as expected can't(won't) solve the problem.

All of the piping is exposed in the basement and appears to be run horizontally and nearly level until it reaches the main vertical drain pipe. The main pipe seems a bit small for the load, but I'm not sure what it should be.

Here is the layout: The washer in SE corner of the house, the sink and dishwasher in the NE corner (about 16' away) and the tub/shower, stool and sink is located dead center on the back of the house. The main line is 6-8" off the ground just below where all this piping meets up. I only have two visible vent pipes on the roof (one should be for the furnace) and I believe that could be my root cause.

Looking at some of the diagrams in the threads the 3 items in the bathroom should be vented up and across to the vent to the roof. I highly doubt that this was done as it appears this was a DIY project by the prior owner.
I also doubt that the kitchen or the laundry area were vented at all. Both are on outside walls, but I don't have the ability or cash to tear out walls etc... Could a studor vent be utilized in this scenario? That may not be the correct term, but an old plumber friend mentioned it.

I want to understand what I need to do, but may not understand all the lingo. I don't want to get stuck paying someone for something I don't need. Some of this I can do myself with a little help.
Thanks,
KJ in Kansas City