Depends on the LED, a red LED has a typical voltage of 1.2V
Green 2.2V, its only the blues and whites whic require > 3.0V. But at 'reasonable' brightness, the current would have to be 15mA, so thats a max of 150mAH/15 = 10 hours.
Charging NiMH is a bit tricky as they prefer to be charged quickly at high current, with charge termination ( a way to stop pumping current into it so it doesn't die). Trickle charging isn't always a good idea. I guess the easiest method would be to use am LM317 as a constant current source, and a comparator to turn off the current once the battery reaches full charge. But you would have to set this threshold a bit below the 'max charge voltage' to make sure you don't' over charge it. And this threshold depends on the charging current and the battery itself
So, without experimenting, its hard to give a figure. Perhaps 1.3 - 1.4V per cell is a cautious number, that's 3.9V for the little batpack.
Its not the best way to charge a battery, but its relatively simple. Adding hysteresis to the comparator would mean it doesn't constantly flutter between charging and termination. The circuit should only turn on when its say < 3.4V, and only turn off when its 3.9V.