Yes, it's still legal to go there, but before visiting, you should check with the US Fish & Wildlife Service (USFWS) and US Coast Guard (USCG). I don't know if USFWS requires any permits for a private citizen to visit, but I believe USCG does require that you receive permission before going on their land. There are areas with unexploded ordinance, so at the very least, that's a good reason for checking in with them. (Most of the land is under the stewardship of the USFWS, but some of the land around Massacre Bay is still under the USCG even though have abandoned the Loran station.)
And yes, to repeat the previous answer, it's not possible to fly there anymore. The only way to go is boat. I've chartered a boat and took a group of birdwatchers there in 2010 and trying it again in 2012 - it's a commercial venture so I had to get permits from USFWS. It's tough finding a boat that can do it for a reasonable price.