Where could one find a table of Helium and/or Hydrogen escape rates through various materials? What is the Physical mechanism: is it tunneling only or other things contribute as well?
You are looking for gas permeability charts and tables, some of which can be found through Google and Google Books (and your local university library). Are you looking for any materials in particular?
I don't have the book handy, but Greenhouse's Hermeticity of Electronic Packages has a lot of useful information.
The mechanism is that a gas atom enters the solid (in crystals, it might occupy an interstitial site or travel down grain boundaries) and randomly moves around. Gas permeation involves many, many gas atoms that diffused through and exited the other side of the material.