I have what is called sciatica (pain running down my leg from a trapped nerve). This sounds like it is what you may have.
They (PT) told me that the treatment options may be either of those three that you have described but they did not say which one would be more effective for the pain.
Below is some websites I found off the internet. Hopefully this should be of some help.
Information on Epidural;
http://www.neurologychannel.com/epidural/index.shtml
http://www.spinalmedicine.com/ask/q021121.html
Information on Facet;
http://www.classichospitals.com/article.asp?article=294
http://www.mayfieldclinic.com/PE-FACET.htm
http://www.spineuniverse.com/article/article1176.html
http://www.wiganleigh.nhs.uk/Library...injection.html
Information on Nerve Block;
http://www.spineuniverse.com/display...ticle1970.html
http://www.thephysiotherapysite.co.u...ve_blocks.html
You will be able to find out more information on these three procedures by using the Google website
http://www.google.co.uk/ and typing them into the search engine.
I cannot answer directly what the best one would be for you as each, I would imagine would be more suitable for a particular case. It would be best to ask your specialist about which he/she thinks would be best.
Good luck with your treatment.