The total energy of a system is called its internal energy.

The internal energy is, then, the sum of the rotational, vibrational, electronic, kinetic and potential energies. Hence, its units are joules again.

Internal energy is a state function. This is a property of the system that is only dependent on the current state of the system - it doesn't matter how it got there. So, if a system starts with energy U_a and finishes with energy U_b, then the change in energy is

ΔU = U_b - U_a