Ass in, could I play this game without picking up 1-3? I just recently picked up the DeSu games and they've got me interested in the series. My PS3 isn't backwards compatible, so going back for the Persona series or for Nocturne doesn't really seem feasible at the moment. My best bet for another megaten he would be this release, but I don't want to jump in if I'm missing too much more than odd references here and there.
Jump right in. Of course, you could try Strange Journey, also on the DS, which is like a cross between Etrian Odyssey and old school Shin Megami Tensei. You have plenty of time to do that... This ain't comin' out no time soon.
The official Uriel of the Shin Megami Tensei IV board. http://myanimelist.net/profile/Moranite
Considering most people haven't played the first two games since they lack a US release, it isn't too awful jumping in mid stream. The stories of each game are not closely connected though they do take place in the same world.
If I were you I'd try to pick up a used PS2 for $50 or less on Amazon/Ebay and Nocturne + P3 + P4 + Devil Summoner 2. All great games and more than worth the purchase of a PS2.
You forgot Digital Devil Saga. Clearly you remembered Raido Vs. the Soulless Army, though. XD
Oops. Yeah them too though I consider the DDS series the worst on the PS2 (still not bad, just not as good as the others. My experience was really hampered by the way too frequent random battles honestly, combined with LONG dungeons. Nocturne was similar but it was different for me for some reason. Soundtrack for DDS1 is one of Meguro's best compositions though.) Also I referred to King Abaddon not Soulless Army (haven't played that one).
Beside some references, every MegaTen game - like most long running RPG franchises - is self contained. Even the Persona games have no real connection except for some cameos. Unless the game itself is a direct sequel, you don't need to play the previous games in order to understand the plot. Most of the games are awesome though, so you should really consider checking some of them out.
Official Masakado of the Shin Megami Tensei IV board... Waiting for: Persona 4 Arena, DS Soul Hackers, SMTIV