host famaily stay

Ok Ken, since two days have passed with no answer, I will bite on this. The term "host family" usually refers to foreign student exchange programs or people looking for a sponsor to immigrate to another country and get legal status. Neither of these options seem likely. If you gave a few more details about what you are really looking for, you might get some replies.

... Not necessarily. I admittedly have no information about Odessa, but I stayed with a host family in St. Petersburg. That was purely as a tourist. I found my lodgings through a company that specializes in Russian travel (although I think they went out of business). That's the first place I would look.