The presence of sewer gas inside a residence is serious, but the cost to repair depends on the cause, some of which can be more severe than others. It’s a major health risk – even a potential explosive fire hazard, if bad enough (and a potential though unlikely asphyxiation problem, as well, if it’s that bad) – so it needs to be remedied soonest.
Causes can range from the ridiculously silly and easy to fix, to major expense items.
Easy: Birds, squirrels or other animals nesting on top of (or inside) the vent pipes that on most dwellings penetrate the roof line as uncapped pipes. The fix is to plumb the vent to be sure that it is clear (and by “plumb” I mean simply lowering a round weight on a string the known distance from the top of the pipe to the drain line), and then covering the vent pipe with heavy screening, secured so that it won’t blow off. That ensures the vents work. If the vent is clogged with anything, then a plumber’s snake will clear most common animal-generated blockages. (Every fixture is vented, but not always with individual vent lines. Individual vent lines, when they exist, are generally “ganged” into a main vent for the plumbing at that point in the dwelling, and the gang vent pipe is what you see when you look at the roof. Every vent has to work, but it’s the roof vent that is most attractive to nesting animals.)
Dried-out water traps are another easy-to-fix problem – assuming that all of the piping is intact and the drain traps don’t leak. (Corrosive cleaners improperly used can accumulate in metal traps and corrode them, which allows them to drain unexpectedly and improperly.) If the space under the sink is ALWAYS dry, and if the sink is used normally, then that may not be an issue.
More expensive fixes could be an improperly plumbed system, with insufficient venting to begin with, clogs and partial clogs in drains, as @johnpowell notes, and broken joints at any point in the drain or vent system. (The reason the vent lines exit the dwelling in the first place is that they DO vent sewer gases; that’s their function. If the vent line is cracked, corroded or open inside the home – and the vent line, being normally dry anyway, may not raise any red flags to someone who sees “no water leak, so it must be okay” – then that’s a source of problems.)
Other problems could be a faulty or worn-out wax seal between the toilet and the floor drain. I noticed this once in an old set-up mobile home that I lived in. The floor around the toilet was “soft”, which felt not-right, obviously, but it was the only noticeable problem at first. Then I noticed that the toilet could “rock” ever so slightly. So my first inclination was to tear up the “bad floor” and replace it with good flooring. That’s when I discovered that the toilet installation from years earlier had been “just a little off”, which cased one of the hold-down bolts to crack, which allowed the rocking, and that started to wear the wax seal (because the was seal is not a “wear” item; it’s supposed to be “set it and forget it”), and the wearing of the wax seal enabled a little seepage of each flush into the wooden sub-floor, which rotted the sub-floor under the linoleum, which worsened the rotting floor and which all kept worsening the problem.
So: Look for wetness where it doesn’t belong – even the least little bit can indicate a bigger problem that’s just not visible yet – and if you can get to the lower level (basement? lower floor? crawl space?) look for dampness or mold, which are indications of a current / ongoing problem, or unexplained staining, evidence of an earlier problem even if it’s now dry. If you venture into a crawl space be sure to have positive ventilation AND someone outside to pull you out without having to enter themselves in case you are overcome by CO2 or other non-breathable atmosphere. (In fact, if you open a crawl space and smell sewer gas, then it’s best to just leave that space open and call a professional.)