U represents the internal energy of a gas. The contributions to U are the kinetic energy of the gas molecules and the energy from interactions between particles. Because ideal gases, by definition, do not have any intermolecular interactions, U depends solely on the kinetic energy of the gas. Since temperature is a measure of the kinetic energy of the gas, we say that U depends solely on the temperature of the gas. If the temperature of the gas does not change, it is neither gaining nor losing any kinetic energy, so it's internal energy must remain the same.

Qualitatively, we can express the relationship between internal energy and temperature as:

dU = C

_{v}dT

where

Also, if you understand that ΔH = 0 for an isothermal process, what will Δ(PV) be for an ideal gas undergoing an isothermal process? Therefore, what must ΔU be?

Finally,

If ΔU = q + w then surely for expansion, since a perfect gas's pressure and volume are not taken into account w = 0.

This statement is not true. Ideal gases have pressure and volume (perhaps you are confused by the assumption that the gas molecules of an ideal gas are assumed to have no volume. This does not mean that the gas itself has no volume). Unless the gas is expanding into a vacuum, w < 0 for any expansion.