If a wasp stings someone on the foot, causing it to swell up, is it ok to soak the foot in some warm water with vinegar and baking soda?

Yes: That is perfectly fine to do. You can also take an antihistamine like Benadryl (diphenhydramine) or claritin.

No: Soak in warm salt water. Seek medical evaluation for a possible infection.

No: No you should avoid heat. Ice is preferred, an antihistamine is also recommended such as benadryl (diphenhydramine). (oral.).

Yes and no: Soaking may make it feel better at first but may cause the foot to swell more. A better course of action may be to ice the area and take an antihistamin such as benadryl (diphenhydramine).