The internal energy of a system is always increased by a adding heat to the system and having the system do work on the surroundings b having the system do work on the surroundings c withdrawing heat from the system d a volume compression e adding heat to the system

There are two correct options:
d) a volume compression
e) adding heat to the system

In fact, we can have a look at the first law of thermodynamics:

where
is the variation of internal energy
Q is the heat absorbed by the system
W is the work done by the system on the surrounding

It is important to keep in mind the right sign convention for Q and W: Q is positive when the heat is absorbed by the system, while it is negative when it is released by the system; W is positive when it is done by the system on the surrounding, and negative when it is done by the surrounding on the system.

Using this convention, we can see that:
d) when there is a volume compression, the work is done by the surrounding on the system, so the work is negative, and the variation of internal energy is positive due to the negative sign -W in the first law of thermodynamics
e) when heat is added to the system, Q is positive, so the variation of internal energy is positive as well