Battle Moveset

A Good Moveset for Porygon2 would have to be this:

Attacks:

Thunder Wave
Ice Beam
Thunderbolt
Substitute OR Recover

Items Attached:

Lum Berry

Preferred Nature:

Modest

Strategy Using Porygon2

Porygon2 is a well rounded pokemon, apart from speed, it has stats that are average - above average. It has a wide movepool available to use, and can learn something to make up for the lack of speed (agility or Thunderwave). Since its special attack is the highest of all stats, special attacking is the way to go (though it could work with a MS like: Return/Tri attack, Thunderwave, Shadow ball, HP Physical. It can even be used as a choice bander, but there are better pokemon available as a choice bander, i.e. Medicham). The last move slot can be Recover or Substitute. Substitute allows for you to buy for some time to use Thunderwave/Agility (though I've heard that Agility, which would make it a special sweeper, doesn't work...) without the risk of getting hurt badly by your opponent. Since Porygon2's stats are already well rounded, the need for a pinch berry isn't such a big deal. Lum berry is needed though to prevent any status damage for seriously damaging Porygon2's abilities. Take note of Porygon2's trait, which allows it to copy whatever characteristic your opponent has, which can come in handy if you switch in Porygon2 when you're expecting a Surf from Mantine/Vaporeon or an Electrical attack from a pokemon like Jolteon/Lanturn.

EV Corner:

Max out the EVs in Special Attack & HP for Porygon2 with any remaining in Special Defense

Strategy Against Porygon2

Porygon2 is one of the most 'user-friendly' Pokémon available, with a nice variety of moves and good stats (aside from speed). Its signature moves 'Conversion' and 'Conversion2' are rarely used, so chances are you won't need to worry about dealing with a multi-typed Pokémon.
- Firstly, keep note of which trait Porygon2 has traced, because it may become a major disadvantage (Example: Water Absorb copied from a Water Pokémon). Also, if you expect Porygon2 to be switched in, arrange your move so that it won't be used in a way that would be an advantage to Porygon2 (Example: Vaporeon vs. Golem, it is a likely bet that Porygon2 will be switched in and can regain health from Surf).
- Thunder Wave tends to be used a lot on Porygon to, however, to counter it isn't as simple as sending out a Ground Pokémon with Porygon2's Ice Beam access. With such low speed, most Pokémon can set up a Substitute before Porygon2 can use Thunder Wave, which has the same effect as a free turn. Failing that, you can use a Pokémon with limber or a fast Ground type such as Dugtrio.
- From there, it's a matter of surviving the commonly used moves (for Porygon2): Thunderbolt and ice Beam, the combination nicknamed 'Bolt-Beam'. Very few Pokémon can resist the combination (The Magneton and Lanturn families are the only ones as far as I know) so your best bet would be to use a Pokémon with High Special Defence (and HP), preferably with a resistance to one of the attacks.
- As for knocking out Porygon2, it's best to capitalise on its weaker Defence and Fighting weakness. If you don't have a Fighting move, just attack either defence, there is only a minute difference between Porygon2's Special and Physical Defences. Also, be aware of Porygon2's access to Recover, don't waste time once you have lowered Porygon2's HP or else your efforts will have been wasted. Stat boosting is advised, especially if you have a Sub up.

Contest Moveset

A good Contest Moveset for Porygon2 would have to be this for the Cool Contest best with Lonely, Adament, Naughty or Brave Nature:

Attacks:

Rain Dance
Thunderbolt
Thunder
Hyper Beam

Items Attached:

Red Scarf

Strategy Using Porygon2

If you do the attacks in this following order you should have very few problems; 1st - Rain dance, 2nd - Thunderbolt, 3rd - Rain dance, 4th - Thunderbolt, 5th - Hyper beam.

Locations in Games

Ruby/Sapphire/Emerald Trade from FR/LG Colosseum Trade from FR/LG Fire Red/Leaf Green Evolve Porygon

Animé Appearences

Porygon2 has yet to have an Animé Appearence