The oldest extant school (and proven..) is the Tenshin Shoden Katori Shinto Ryu founded around ca.1447 by Iizasa Choisai Ienao and still practised in Chiba prefecture, Japan.
It contained Kenjutsu (odachi,kodachi,ryoto), Iaijutsu (with Odachi), Bojutsu (Rokushaku Bo), Naginatajutsu (with Onaginata), Sojutsu, (with Su Yari), Jujutsu, Shurikenjutsu, Ninjutsu, Chikojojutsu (Castle attack/defense strategy), Gunbaiho (Tactics), and In-Yo Kigaku (Yin/Yang divination).
Emphasis is centered on the Odachi and the school has a wide variety of Iaijutsu techniques..most from standing although a few are from Iai-goshi (a 'seated' posture familiar to this school.)
The Shinto-Ryu is the oldest proven school and has maintained it's curriculum almost intact since it's founding.
Hope this answers your question.
P.S. The Shinto Ryu website address is www.katorishintoryu.com