4x4 Parity Algs
Edge Flip W/O messing up cross (for Yau): Uw R U R' F R' F' R Uw'
Edge Flip w/ messing up cross (for reduction): Uw R F' U R' F Uw'
OLL Parity: Rw U2 x Rw U2 Rw U2 Rw' U2 Lw U2 Rw' U2 Rw U2 Rw' U2 Rw'
PLL Parity: Uw2 Rw2 U2 R2 Rw2 U2 Rw2 Uw2
To Avoid triple Parity on 6x6 = 2R U2 x 2R U2 2R U2 4R' U2 2L U2 2R' U2 2R U2 2R' U2 2R'
All these algs can be used for bigger cubes you just have to grip more layers.