The most unusual Gen 3 team I ever had was probably my Sapphire team from a couple of years ago, the team that was decided by the Pokemon cards. I didn't know what team to use for this playthrough and I had a few unopened packs of Pokemon TCG cards from the few most recent sets at the time so I decided to open them and use the first 6 fully evolved Pokemon I pull from the packs, first 6 that are catchable in Hoenn of course. So my team ended up being:
Weird team but it made for a very fun and challenging playthrough. Beating the first half of the game with just Masquerain and Sableye was an interesting experience. And then in the E4 and Steven fight it was Heracross that helped me win because the rest of my team was just too weak and/or too underleveled to do any significant damage to Steven's Pokemon.
I often did solo runs with Swampert back when Emerald was my only game. My best team for Hoenn has to be my most recent, from about 5 years ago:
I'd literally never caught a Feebas before, so that was very rewarding. I had to wait until the post-game to blend with Berry Master in order to evolve it. During the story I also used Absol - a great design let down by his stats and typing being at odds - and Clamperl, the latter because when I caught one in a Dive Ball it turned out to have great IVs and Hidden Power Grass, which made it brilliant against Juan and Wallace. Its now in Gen V as a Gorebyss with Shell Smash. Torchic was my first ever starter, and I remember thinking Blaze Kick was incredibly cool, but I'd only ever completed the game with Swampert until then (still never even evolved a Sceptile).
The five pictured (except Clamperl) each reached Master Rank in contests, as well as doing quite well in Battle Frontier (I think I may have beat the Dome Ace): Cool, Cute, Smart, Tough, and Beauty respectively.
I did a LeafGreen run with Red's team from PokéSpe which was quite cool, but not particularly challenging - Venusaur, Pikachu, Poliwrath, Gyarados, Snorlax, and Eevee then Aerodactyl is not exactly a weak team. Now Gold in HeartGold on the other hand...that was tricky! No Fly, for authenticity I didn't evolve Aipom (and couldn't Togetic), not a single super-effective move to hit Dragon (although Sudowoodo could get a hit in on Charizard)...might do it again in the VC release!