Seva, as Talesof stated above a few more pictures would be needed for further critiquing of your table.
From the above picture it doesn’t look to me like it is made of walnut. “Utility” tables were not often made of walnut. If it was American made, ……. and I say that because there have been quite a few posters of lately from the UK, etc., that have been fending questions on this Forum, …… then I will venture a guess that it is made of poplar, circa 1800’s, because of the “simplicity” of the design/construction and the “tabletop” board looks to be a “4-quarter” board (4/4” or 1 inch in thickness).
If one knew how all the wood pieces were “joined” together then its age could be better guessed at. And the “value” of such a piece depends on the locale. It should sell for more in the East or North East than in the South or South West, US.