Can you use a smaller bulb with a bigger ballast or vice versa?

In general the simple answer is NO.

A 150w halide would require a 150w ballast, and would not work on a 250w ballast.
Now with fluorescents this can get a little more complicated. You can overrun certain tubes on a larger ballast to get more output from a tube but this will reduce the life of the bulb and the fixture. You would also be risking your safety by not running the correct bulbs in the correct ballast to the manufacturer’s specification. Any warranty would be void.

If you wish you can for example run a 39w T5 on a 38w T8 ballast with the use of T8-T5 converters, however the ballasts are a different type and it is not recommended.