What sort of plug do you have , one of ours has one with a removable filter thing that gets gunged up , if you can remove that you can then clean better from the sink end IYSWIM . I use a folded up wire coat hanger on mine , amazing the amount of crap that you can fish out .
Bicarb and vinegar look spectacular fizzing up, but they cancel each other out as one is acid and the other alkali. Get a sink plunger and stuff a damp cloth in the overflow and give it a good plunge. Any smelly blockage should dislodge.