First, Jynx can appear wherever it wants as its controversy is over, they changed her to purple and she's now in the clear.
FUN FACT: The episodes that
Xen mentioned are important episodes for Jynx. First, in an early Hoenn episode ("
All Things Bright and Beautifly", the episode where May gets inspired to become a Coordinator from watching a character of the day's performance with their Beautifly) there is segment where a filler trainer uses a Jynx but it was cut from the dub as it was still the black Jynx. Much later a character of the day name Erica which was May's rival for the Pacifidlog Contest use a Jynx which was the debut of its redesign ("
Mean with Envy" and "
Pacifidlog Jam"). Though those might better remember its redesign from its next and as of right now most recent appearance, the Battle Frontier episode "
Three Jynx and a Baby" where 3 Jynx go on a rampage through a town because Team Rocket stole their little sister Smoochum.
Now for Kadabra I don't know what's going on with the lawsuit, some say its over in the Pokemon's Company favor while others says it's still going on. Eitherway it hasn't appeared in any merchandise or the anime since the Advance generation (infact in the TCG all Abra cards after Skyridge (last time there was a Kadabra card) are given a PokeBody to instantly evolve into an Alakazam), though I think for promotional pieces and the games they still appear. From what I can read, Uri Geller just seems upset that something who's name is based on his has symbols that sort of looking like Nazi imagery (though you'd think a self-proclaimed psychic would recognize the Zener card symbols... those are 3 wavy lines on its abdomen, not two S's). Not sure if removing/replacing the symbols would help resolve the case. But eithercase, they probably don't want to do anything major with it that could be potentially used against them or reopen the case.
Now Kadabra's limited use was due to a lawsuit, but Porgyon's is probably out of respect for victims. The Porygon controversy was a major controversy at the time, it almost ended the anime (and afterwards they needed to add flashing light warnings to the games). Also respect is an important aspect to Japanese culture, so lengths to show respect is more ongoing. Thus to respect the victims of those who had seizures they excluded anything specific to that episode from being in the anime: the flashing effect, Dr. Akihabara, and Porygon (plus its family). It's also why Earthquake and Magnitude haven't been seen in the anime after the earthquakes in Japan (which also resulted in a few unreleased episodes of the anime).