Don't be fooled: you needn't close any quicker on a REO than you would for any other property.
By the way, if you're not working with a realtor already, then you should probably find one with REO experience to help you to write up and submit your offer.
You can find some lists of REO's on bank websites. You may also try NHMSI.com for HUD homes and ocwen.com for VA homes.
Your best bet is to enlist the help of a local buyers agent. They will have access to these properties and can help you with purchasing one. There is no additional cost for representation, so I definitely would not do it alone.
Yes, you can finance an REO. Preapproval is good.
A better way is to get a realtor to work on your behalf to find the REO's in your area that meet your criteria. That way you have someone on your side as you negotiate with the owner/bank. Remember that most banks holding these properties do not follow the same rules that you and I follow. They are governed only by national, and sometimes international, laws. Very few REO's will actually be good deals as far as value. The realtors who watch the market in your area will know when one is coming on and those properties will be bought quickly by investors who have realtors watching out for them.
We are expecting a flood of properties to come on the market sometime this month as FNMA releases some of the ones they've been holding over the winter. I, and half the realtors I know, am ready to pounce.