You mean by mage, warrior and that? I am not really that much into MMOs myself, but I think I can do it.
Both Kirito and Asuna would be some kind of Berserker, speed based assasins. Endurance is not their strength, in a long fight they would tend to struggle. The fastest they can overcome their enemies, the better. Asuna changes this role for one similar to Leafa in ALO.
For Lisbeth, I dont know. Maybe some kind of offensive tank? She doesnt seem to wear revealing armor, and in MMO those give the best defensive stats. Plus, a mace would make it so she can endure long fights.
Silica would be some kind of buffer. Pina has stat buffs (or so I suppose) and heals. Lets keep it real, guys, as much as we all love Silica, her fear of plant monsters would keep her away from damage duty.
Leafa is the typical perfect mixture between a damage dealer and a healer. She has both a katana, kendo to back her up and healing skills to heal herself/the party. Mixed role, attacker, not as offensive as Kirisuna, and healer.
Sinon is the typical ranged character that provides support from affar. Similar to a mage, without being one. In ALO, they never say anything about buffs and such, but she would be the archer, with lots of hiding buffs.
Klein is similar to Leafa, but more attack oriented. Neither his SAO nor his ALO salamander avatar have healing capability, so he is like Kirito, but arguably more badass due to him using a katana.
Agil is a tank. The guy who grabs a huge weapon and sits in front of the fight, eating damage and aggroing. Nothing more to say.
Going into more side characters now. These are(mostly) gameverse characters.
Philia and Argo are supposedly similar. Average assasin, using a dagger/claws to get next to their opponent without being noticed.
Rain is the same as Kirito, but with a badass skill with a sword overload.
Strea is like Kirito, a berserker, but with HP to back that fighting style. Basically, grab something sharp and shiny, go forward, swing it and laugh at your enemies.
Seven is a dedicater buffer/healer, at leats in the games.
Tia is a rapier user, but one who takes things slowly. Think of ALO Asuna, but without her level of performance.
AAAAAND then we have the Alicezation characters, but describing them would be spoiling, and I dont know if you have read Alicezation yet, so if you want me to somehow say what they are, just say so.
Note that I dont really play MMOs, played Guild Wars 2 for two days before getting bored. And if this isnt what you askrd for, this is gonna be awkward.