Reformatting for an answer:
- OIS (vols) - vols backed out of/for pricing in the presence of multiple curves
- LIBOR (vols) - vols backed out of/for pricing in the 'old' way where discount=forward and basis is negligible
- Black (vols) - Black-76 inverted volatilities
- Normal (vols) - Normal/Bachelier (?) inverted volatilities
FINCAD primer on the 'new curves math': http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2311745
One would not want to drop an OIS vol into an old LIBOR Market Model, but Fabio Mercurio and others have extended LMM to encompass multiple curves with deterministic or stochastic basis functions. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1621547
Various parties quote vols both coming from a LIBOR- or an OIS- space, the Bloomberg function VCUB fits a volatility surface and interpolates and ticks out vols in both OIS- and LIBOR- spaces. Hovering over the various grid points on the various pages of VCUB should be a good place to start for pulling in vols into your own LMM model. A good test of whether you are using the right vols in the right places (and of everything else in your pipeline) is to try and recover the prices/premia of caplets/swaptions that you initially fed into VCUB. And as others have mentioned, being persistent on <HELP> can quickly get you in touch with some very knowledgeable people.