I have two strong parties (all Level 100).

Party #1: Giratina (Origin Forme), Dialga, Palkia, Machamp, Articuno, Mewtwo

Party #2: Ho-Oh, Lugia, Shiny Crobat (Zubat from Cave in FireRed), Shiny Kricketune (from Trophy Garden in Platinum), Shiny Raichu (from Pichu GameStop event), Shiny Gyarados (from Lake of Rage)

I don't use Action Replay, so I ran into and caught Crobat and Kricketune unexpectedly out of pure luck in which I didn't even chain for Kricketune. All the Pokemon I mentioned are legitimate and qualify. Which party should I use if either? Would I stand a chance?

Have a strategy.

That's my first advice, having a party with level 100 Pokémon isn't enough.

Use Jynx and Mr. Mime.

I agree. Part of the reason why i was never able to play competitively even back when i chated like hell was because my strategy is power+speed+element match = win. For people really determined, a good strategy is  needed. A description of move lists for all of them would help.

I don't find any fun in using legendaries. They're pretty predictable anyway.

I thought the world championship standard play was doubles. In which rain dance and trick room teams rule. Also you want to check the rule set first. You have a lot of ubers on both teams which may make your team illegal for competition.

Pokemon isn't about muscle it is about strategy. Your team needs to have a strategy and some form of coherence.

Take for instance a sun team. You have a lead set up stealth rocks (spikes or toxic spikes) then sunny day, and then it uses uturn or baton pass to your sweeper. Your sweeper then knocks out your opponents team and you win. In actuality this doesn't happen but this is your gameplan. You have backup plans if things don't go like you hope but if they do you keep to the plan.

Your team needs cohesion. Which pokemon backs up who? Who is covering your Swampert weakness? Who is stopping Metagross, Scizor, or Gyarados? Who makes it safe for your sweeper to switch in? Who is your sweeper? Who is your wall? Who is your lead? Those are things that need to be asked and considered.

My Machamp knows Rock Slide, Dynamic Punch, and Earthquake, so that takes care of most of the Steel-type, Bug-type, and Flying-type Pokemon. As far as Scizor goes, my Dialga's Overheat move would wipe it out.

You should get another non legendary like snorlax, in case you can`t use them.

Snorlax is also a great tank against special types, shuckle is also a nice tank and attacker if used correctly.

The pseudo legendaries are nice if you only use 1 or 2 and know how to keep them safe from their x 4 weakness. A pokemon with lightscreen and other status changers can be helpfull.

And watch out for a water/ice/electric attack user for your second team.

Edit : magnezone/electvire are also nice pokemon to use instead of a raichu.

A spiritomb can also be fun.

I looked it up and it said that I can use two of the conditionally allowed legendaries which are in my first party. I guess I would let go of Palkia and Mewtwo and replace them with Latios and Suicune if I have to make a choice. And I don't use Normal-type Pokemon by the way.

A shame really, normal pokemon can be really great :P Though i only use munch/snorlax myself :P Great spc def and health, only 1 weakness and the abilty to learn multiple elemental moves.

Thats why snorlax is used in a lot of tournaments.
Substitute is quite a nasty move if used right xD