Is it normal to have numbness in groin/ buttock area 6 days after epidural steroid injection of l3/l4 nerve?

No. This is not the usual outcome check back with doctor a few hours of numbness is normal, buttocks dosent make sense for site of injectionl3-4 is front of thigh L3 can be groin.
It can be. Usually this will resolve once the irritation of the nerve improves. If you are net better after about 7-10 days then consider speaking with the doctor about your concerns.
Not really. Though there could have been some underlying nerve damage at this area to begin with, the local anesthetic agent should have resolved by now. Consult the physician who put this block in and ask what you should do now.