I am building a solid oak rustic table from 4 oak beams and I want to know if I should bother to wax boards on the bottom face in order to protect them (like keeping humidity and avoiding woodwork attacks) or should I apply the wax only on the visible areas and keep the rest raw, maybe even not sanded at all.
No you don't have to bother waxing the bottoms. You can if you want to but it isn't needed, it won't help prevent expansion from humidity (a wax finish is much too thin to provide a seal against moisture) and won't help improve stability.
Even if you were using a much better moisture-excluding finish like shellac or varnish finishing the underside of tabletops isn't as beneficial as most of us assume. Here's Bob Flexner on the subject, Finish Both Sides? Not necessary.
As far as leaving the other surfaces unsanded, that's up to you. As many others do these days I finish all surfaces about equally, regardless of whether anyone will see them or feel them. Other woodworkers aren't fussy about this and only put the full effort into show surfaces. This may seem lazy to some but there is actually a lot of precedent for this as in the past it was commonplace not only to leave the backs of pieces unfinished they were frequently not even made flat and smooth!