If anterior horn spinal nerves are motor, then epidural steroid inj's can only relieve sensory symptoms being injected posteriorly?

Maybe: A far lateral approach to an interlaminar epidural has been shown to provide anterior spread and likely works as well as a transforaminal epidural injection.

Epidural: An epidural is done correctly the medicine surrounds the nerve roots coming out of the conjugation hole. The roots are composed by a motor branch from the anterior horn, and a sensory branch from the posterior horn +/- sympathetic component from the lateral horn. The "steroid injection" reduces the local inflammation which reduces the pain. Can be combined with local anesthetic for prompt relief.

Interesting Thought: The plan is for the epidural steroid injection that is done posteriorly (called interlaminar/translaminar epidural injection) to reach the anterior epidural space where both the motor and sensory nerves exit out. Below the level of L2, roughly the spinal cord ends and all nerves exiting from the spine have both sensory/motor components.