On lowness of $\oplus P$
Weak complexity classes will satisfy $\mathcal{D}^{\oplus P} = \oplus P$. For example, $P^{\oplus P} = \oplus P$.

Strong complexity classes will satisfy $\mathcal{C}^{\oplus P} = \mathcal{C}$. For example, $\mathsf{PSPACE}^{\oplus P} = \mathsf{PSPACE}$.