Gladiator:
剣の喝采 - ken no kassai - literally "applause of the sword" or something like Sword Cheer
Lancer:
鼓舞 - kobu - Inspiration
気合 - kiai - Yell (the term is used in martial arts) or Warcry
竜剣 - ryuuken - literally Dragon Sword/Blade, could be Lancet as mentioned (but used in FFXI as Spirit Surge)
足払い - ashibarai - Leg Sweep (used in FFXI)
Pugilist:
口笛 - kuchibue - Whistle
盗む - nusumu - Steal (used in FFXI)
貫手 - kante? - literally penetrate + hand, something like penetrating blow?
地烈斬 - chiretsuzan? - earth + violent/furious + cut/kill; could be something like Earth Crusher, appears to be an AoE weapon skill where you send a "sonic boom" along the earth's surface delivering a ranged earth type attack.
Marauder:
不屈の行軍 - fukutsu no kougun - Persistent/Fortuitous March, Fortitude March or whatever
丸太割り - maruta wari - Log Splitter? Wood Chopper?
Archer:
影縫い - kagenui - Shadow Stitch (enemy is bound by shooting its shadow)
羽羽矢 - babasa? - Wing(ed) or Feather(ed) Arrow/Shot?
Thaumaturge:
幽遠 - yuuen - literally "deep and remote", not sure what could be fashionable translation for this.
Sorcerer: (ソーサラー/sorcerer is given in the article)
血の儀礼 - chi no girei - lit. "courtesy/honor of blood", maybe something like Blood Honor
荊棘 - keikyoku - briar patch/thorn(s)