Yes Taq, Strange Journey is called Shin Megami Tensei: Strange Journey. It's the closest SMT game to Nocturne since Nocturne, after all the spinoffs since then.

You said you like Puzzle and Action games, so I'll just focus on a few of those.
Planet Puzzle League should be right up your alley. You've probably played some version of this before (Tetris Attack, Pokemon Puzzle League, etc), but the DS version I think is the best one they've done yet. The stylus control really makes it much more active. Picross 3D also came out in the US just this week, and it is also awesome (though less action focused).

Kirby's Canvas Curse is the game that really sold me on the platform. If you got your DS after 2005 there's a chance you missed out on this, so go back and play it.

I love the Ouendan series (which includes Elite Beat Agents), I love Rhythm Heaven, I love Daigasso! Band Brothers (coming out as Jam with the Band in Europe in 2 weeks!). I imported these from Japan originally, but now (or soon) there would be some version of them all available to play in English. And that was my Rhythm Action section.

You're a budding anime nerd, so if you do want to import a game I'd strongly recommend Jump Ultimate Stars. It takes all of the Shonen Jump manga stars (from Dragonball, Death Note, D.Gray-man, etc) and puts them in a sort of Smash Bros-style fighting game against each other. If you're afraid of importing, then the 2nd Bleach DS fighting game (which is more of a Guilty Gear styled game than JUS) is recommendable. The 3rd Bleach DS game is not a fighting game.

Other action games that I can recommend: Space Invaders Extreme, fantastic remix of the old classic. Bangai-O Spirits for just pure action. You can create your own stages in Bangai-O as well as share them with others in a ghetto-fabulous way.

I mentioned in another thread a while back that I'll make my own comprehensive DS recommendation thread one day. These are some of the games that would be on there.