I've done a Knife block in red oak to replace our run down old block.

What type of finish should I use in order to sustain kitchen environment
(water, grease, bacteria and god knows what) ?

Red Oak is extremely porous. I would opt for a good film finish,
probably a Poly. Some folks may steer you towards a mineral oil finish,
such as used on cutting boards but I think Red Oak is just too porous
and should probably be sealed.