The moemon dragons aren't obtainable and were never meant to be used by the player- that's why there's no documentation. I went ahead and grabbed the stats for them though:
Salamence- Dark/Illusion, Intimidate, 95/135/80/110/80/100
Garchomp- Earth/Illusion, Intimidate, 105/130/95/80/85/105
Gyarados- Water/Flying, Intimidate, 95/125/80/60/100/80
Charizard- Fire/Flying, Blaze, 80/85/80/110/85/100
Dragonite- Flying/Illusion, Speed Boost, 90/135/95/100/100/80
Rayquaza- Wind/Illusion, Levitate, 105/150/90/150/90/95
Giratina- Ghost/Illusion, Pressure, 150/100/120/100/120/90
Palkia- Water/Illusion, Intimidate, 90/120/100/150/120/100
Dialga- Steel/Illusion, Intimidate (changed to Focus in Emerald), 100/120/120/150/100/90
Latios- Reason/Illusion, Speed Boost, 80/90/80/170/150/110
(stats in HP/Atk/Def/SAtk/SDef/Speed order)
In Fire Red 1.8, Lance uses the first five in his normal battle and the latter five in the rematch. In the first fights they have unedited movesets, so you get to deal with ridiculous movesets like Thunder Wave Charizard- in the second fight their movesets are edited but with little respect for what the mon actually learns (Hydro Pump Dialga ahoy). They are all unobtainable and were never meant to be used by the player- they don't even have backsprites or proper movepool data.
Emerald 1.8 (which is what it looks like you're playing) handles them similarly- most of them are lurking in the Battle Pyramid's later rounds though. They're also still unobtainable and will almost certainly remain that way. Since the wiki is mostly meant as a reference for playing on Shoddy, it leaves them out as they have no place in competitive battling.
As far as the IV checking goes, I checked CAya and CHatate's pages on the wiki- they're accurate. Would you mind posting the stats and natures of some puppets that don't check out for you? Also make sure you're using a puppet that doesn't have any EVs- while you can IV check one that has been EV'd it's a lot easier to mess up.