Will an epidural steroid injection improve elbow pain that I get when I workout.?

Likely no. Most elbow pain is from issues in the elbow. Unless your pain is coming from your neck (unlikely if just elbow pain) an esi will not help. You may need an injection in the elbow.
NO. Unless your elbow pain is part of a referred pain from spinal stenosis or a component of radicular pain from a disc herniation an esi will not help. You should be examined to determine the exact cause of your isolated elbow pain.
No. epidurals are performed on the spine not an elbow.
Well. Hard to say. If the elbow pain is due to a pinched nerve in the neck, then it might help. If the elbow pain is due to injury at the elbow then epidural injections are not going to be helpful.