Lorelei
The first member of the Elite Four you will face is Lorelei, who uses Ice- and Water-type Pokemon. She has a Level-52 Dewgong, Level-51 Cloyster, Level-52 Slowbro, Level-54 Jynx and Level-54 Lapras. Water-type Pokemon are particularly weak to Electric-type moves, so use an Electric-type and you should be able to take down all five without much difficulty.
Bruno
The next foe is Bruno, who uses Fighting- and Rock-type Pokemon. He has a Level-51 Onix, Level-53 Hitmonchan, Level-53 Hitmonlee, Level-54 Onix and Level-56 Machamp. A strong Water-type Pokemon should take care of most of them, the Onix in particular being very weak to Water-type attacks, but the Machamp is dangerous. It's weak to Psychic- and Flying-types, but can deal massive damage to Flying-types with his Rock Tomb move. Keep using Psychic-types, but you'll need to heal and swap out Pokemon a few times.
Agatha
The third member of the Elite Four is Agatha, who uses Ghost- and Poison-type Pokemon. You'll need a few good Antidotes in your medicine bag for the Poison moves. Her Pokemon are a Level-54 Gengar, Level-54 Golbat, Level-53 Haunter, Level-56 Arbok and Level-58 Gengar. Normal- and Fighting-types won't work on the Gengars and the Haunter, but they're weak to Ghost-, Psychic- and Dark-type moves. The Arbok is weak to Ground- and Psychic-type attacks, and the Golbat is weak against Rock, Electric, Psychic and Ice.
Lance
The final member of the Elite Four is Lance, the "Dragon Champion." His Pokemon are all Dragon-type -- a Level-56 Gyarados, two Level-54 Dragonairs, a Level-58 Aerodactyl and a Level-60 Dragonite. The Gyarados is very weak to Electric-type attacks, while the other four are all weak against Ice- and Dragon-type attacks.
Champion Gary vs Bulbasaur
Having defeated the Elite Four, you now face the Pokemon Champion, Gary. His Pokemon change depending on your starting Pokemon. The first three are always a Level-61 Pidgeot, Level-59 Alakazam and Level-61 Rhydon, which are weak to Electric-, Bug- and Water-types respectively. If you chose a Bulbasaur, the next three will be a Level-61 Exeggutor, Level-64 Gyarados and Level-65 Charizard. Exeggutor is extremely weak to Bug-types, while Charizard is weak against Rock, Water and Electric.
Champion Gary vs Charmander
If you chose Charmander, Gary's first three Pokemon will be the same as above, but he will then send out a Level-63 Exeggutor, Level-61 Arcanine and Level-65 Blastoise. The Arcanine is a Fire-type that is weak to Ground, Rock and Water, while the Blastoise is a Water-type that is weak to Electric- and Grass-type moves.
Champion Gary vs Squirtle
If you picked Squirtle, Gary's first three Pokemon will be the same as above, but he will then send out a Level-64 Arcanine, Level-61 Gyarados and Level-65 Venusaur. Arcanine and Gyarados are covered above, and Venusaur is a Grass-type Pokemon weak against Flying, Fire, Psychic and Ice.