I believe you’re talking about an “S trap” under your sink which is not a permitted type of plumbing installation. Water that is filling the downstream of a vertical portion of the S trap is often responsible for siphoning and sometimes loss of trap seals.
This means that water flowing down the pipe will create vacuum and suck all the water out of the p-trap section. That little bit of water inside the p-trap creates a seal which blocks sewer gases from entering your home.
Missing plumbing vent is another serious issue and taking care of the vent and the “S” trap would most likely take care of an unpleasant odor in your house. Unless there are some other plumbing issues you might not be aware of…