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I have been gone from Warhammer Fantasy for quite a while, well before 7th edition. Is the Storm of Chaos book still usable, or are those rules invalid now?

It's up for debate. At least one GW tournament has said it's unusable, others have said it is usable.

The army lists in it are being slowly replaced by new Army Books such as Orcs and Goblins, High Elves, and the Daemon army book coming out next year. I personally wouldn't make a SoC army at this point in time unless I could also use the normal list for it.

The only 'eternal' list is supposed to be the Slayers, thanks to GW's 'divine' intervention. The Cult of Slaanesh is likely to be around a while. DE always get the dirty end of the stick, but they like it.
(Of course Chaos Dwrf have almost forgotten what the stick looks like)

O&G
Empire
Dwarfs
High Elfs

are all out, invalidating their lists.

Vampire Counts are next.

Clan Eshin will also be around for a couple of yesrs.

There's been preview models shown for DE already. I'd expect them sooner rather than later.

True, but 'sooner' may well be early 2009!

The lists are available here.

http://us.games-workshop.com/games/warhammer/stormofchaos/gaming/default.htm

I'm not sure what the legality of the various lists is.

Generally, from what I've seen, the non-"official" (ie non GTs) tournaments may allow at least those SoC lists which have not upgraded their army book since Storm of chaos was published, but in the end it's up to the tournament organizers. Changes are that GT's have banned all of them (not sure about the US circuit, though).