What is the effective temperature of a fully shaded object in earth orbit?

Don't know exactly, but even if a cryogenic object is shaded from the sun, the reflected light from Earth actually is a measurable factor when dealing with very cold temperatures. Was privy to some of the work on the Gravity Probe B telescope, which functions at temperatures near absolute zero.

Given the small mocular radius of hydrogen, how can the high leakage rate be overcome?

Hydrogen is actually less of a leakage problem than helium, since it tends to link into two-atom molecules. That doesn't mean it's insigificant. I'm not an expert in this particular field, but there are experts studying the problem. It has application for many areas other than spacecraft.

When we talk about long term storage, are looking at days, weeks, months or years?

Days would be a minimum for Earth orbit. Longer times can be achieved by either active cooling systems or highly advanced insulation. Neither would be lightweight.

I know they were looking at modified Centaur engines for lunar missions.