How to dispose of junk and valuables in foreclose home

I just bought a home at auction.? It is full of personal possessions
including furniture, stereo equipment etc.? What are my
responsibilities towards the previous owners.? Do I have to hold a
formal auction to sell this stuff or can it be given away or dumped?? According
to neighbors the previous owners have been gone for almost 6 months.

Yes, if it is worth more than $300 you do have to auction it. See CA Civil Code 1980 for details, including the notice you need to post and publish. Do note that you can move and store the property at their expense (meaning they’ll have to reimburse those costs >if< they reclaim it). If they don’t reclaim it, then you can auction it, and you get to keep the amount of funds necessary to repay your moving, storage and auction costs.
If at all possible try to track down the folks and get them to either pick it up, or give you something in writing that you can dispose of it.

Can I conduct this auction myself or do I need to hire a licensed auctioneer?? If I do it myself is there any particular rules about how the auction should be conducted?

As I recall they need to be licensed. You may want to call some storage folks. They regularly hold personal property auctions for unpaid units. You could probably work a deal with them where they pick up the stuff, store it, auction it, for a set fee, with the proceeds going towards their fee and you guaranteeing the difference if any. ? I’ve only had to do a couple. We did it all ourselves and had a licensed auctioneer just onsite for an hour to call the auction.