Bleach can work, and if you could mix in some googone to help with
releasing some dirt and oil, that will help, but only a little bit.
Homedepot sells a grout scrubbing brush that'll keep you off your
hands and knees. It would also be good if you have a shop vac to
clean up all the slurry that will be on the floor. Don't forget to
get a face mask because those fumes can be awful. The outcome of your
hard work can only be determined by the amount of neglect your T&G has
recieved over the years. Def. seal your grout when you're done. We
only use solvant based sealers when working with man made tiles. The
labor will be intensive and time consuming, if all else fails, hire a
professional.

P.S. If grout is mixed and installed properly, it can withstand up to
2000+psi w/o harm. It's what my company uses on a daily basis.

GL!!!