You likely have multiple issues like lack of a p-trap and a plumbing vent. You are better off waiting for a time you can afford a plumber because this repair has multiple layers of issues.
Folks, home inspections are supposed to point these things out. Never buy a house without having an inspection.
In our state, there are required disclosures for all known defects.
Keep ventilation to a max. in the bathroom because sewer gas is not healthy and I am sure the sewer gas is permeating your living space.
Additionally, PVC is not permitted for use as water pipe in dwellings because it cracks very easily causing enormous damage. Looks like you have PVC water pipe.