Sokcho to/from Seoul
There is no train that directly services Sokcho. There are however bus options from both the Dong Seoul Bus Terminal and the Gangnam Express Bus Terminal. Total journey takes around 4 hours. Departures are about every hour. The buses don’t have toilets or amenities, but make at least one stop.
from Gangneung to Sokcho
One can take the bus to Sokcho from the Gangneung Express Bus Terminal. As of April 2007, a bus leaves Sokcho every 30 mins and the trip lasts for an hour and 20 mins. The ride is quiet comfy though there's not much to see along the way.
Express Bus from Ulsan to Sokcho
I was plesantly surprised to find a bus that leaves from Southern Ulsan to Northern Sokcho. It only cost me about US$25 or so to make that long 7 hour journey.
Take note that you'll need to change buses at GangNeung though. I wasn't aware of it till the last minute - Thank God there was a kind bus driver who looked out for me. He pratically carried my bag and guided me to the next waiting bus.
The bus leaves Ulsan Inter-city Bus Terminal at 10.30am sharp.
You can take number 7 for seorak mountain.There is a bus from sokcho-city to seorak mountain. It takes 20min to Mt,seorak.