If you listen to Social Distorton,

They are punk. I also listen to The Vandals, Flogging Molly, Guttermouth, The Clash, The Sex Pistols, X, X-Ray Spex

Yes they are punk. like above has said. Like their music good band. Vandals are great at a concert.

I'd actually classify Social Distortion as a mix of punk/rockabilly, as opposed to straight up punk rock. If you like them, there's a ton of other bands that play in a similar vein...check out www.hell-cat.com, which is an indie record label who has mostly punkabilly or ska-punk bands.
If you've never listened to Operation Ivy or Voodoo Glow Skulls, you might take a listen.

Yup, I agree punk/rockabilly. I've loved them since I was a preteen...I'm 36 now. I also listen to the Ramones/The Clash/Hagfish/Poison idea/Alkaline Trio ect.....