1. I took a long list of 4x4x4 parity algs created by Kare Krig. They can be found here: http://apelgam.se/Rubik/4x4parity/

2. I pasted every alg into http://alglister.whocouldthat.be/ (created by Justin Jaffray upon personal request). It sorts all the algorithms out in QTM.

3. Then I took every short alg and tried all of them out including their mirrors, inverses, AND mirror inverses.

4. Then I was left with these algs which I feel are worth learning. I did not bother searching through any of the algorithms that affect more than one F2L slot because it's difficult to detect OLL parity for me before that point.

I have sorted the algs out by how much they affect F2L, from the least to the most.

Please let me know if I have made any mistakes and happy learning!

Flips one edge:

Algorithm and length (QTM) | Effect |

Rw' U2 Rw' U2 Rw' U' R' Rw' U2 R2 U' Rw' U' R' Rw2 U' Rw' U Rw' (24) | Flips UF, antisune affect on corners |

Rw' U Rw' U' Rw2 R' U' Rw' U' R2 U2 R' Rw' U' Rw' U2 Rw' U2 Rw' (24) | Flips UR, antisune effect on corners |

Rw' U Rw' U' Rw2 R' U' Rw' U' R U2 Rw' U' Rw' U2 Rw' U2 Rw' (22) | Flips UF, shoots DFR to RBU |

Rw' U2 Rw' U2 Rw' U' Rw' U2 R U' Rw' U' Rw2 R' U' Rw' U Rw' (22) | Flips UF, shoots DBR to FRU |

Rw' U2 Rw2 U' Rw U2 Rw' U2 Rw U Rw2' U2 Rw2 R U' R' U Rw (25) | Flips UB, brings out BR pair |

Rw U2 Rw2 U Rw' U2 Rw U2 Rw' U' Rw2 U2 R' Rw2 U R U' Rw' (25) | Flips UF, brings out FR pair |

Rw' U' R U R' Rw2 U2 Rw2' U' Rw' U2 Rw U2 Rw' U Rw2' U2 Rw (25) | Flips UR, affects BR pair |

Rw U R' U' R Rw2' U2 Rw2 U Rw U2 Rw' U2 Rw U' Rw2 U2 Rw' (25) | Flips UR, affect FR pair |

Flips three edges:

Algorithm and length (QTM) | Effect |

Rw' U' Rw' U2 Rw' U2 Rw' U' Rw U2 r U2 Rw U' Rw' U2 Rw' U2 Rw' U' Rw' (28) | Flips UF,UR,UB, (Pure!) |

Rw' U R U2 R' U' Rw' U2 Rw' U2 R Rw' U' R' U2 R U' R' U2 Rw' (25) | Flips UF,UR,UB, twists DFR |

Rw U2 R U R' U2 R U R' Rw U2 Rw U2 Rw U R U2 R' U' Rw (25) | Flips UF,UL,UB, twists DFR |

Rw' U2 R' U' R U2 R' U' R Rw' U2 Rw' U2 Rw' U' R' U2 R U Rw' (25) | Flips UF,UL,UB, twists DBR |

Rw U' R' U2 R U Rw U2 Rw U2 R' Rw U R U2 R' U R U2 Rw (25) | Flips UF,UR,UB, twists DBR |

Rw' U' R' U' R U' R' U2 R U' Rw' U2 Rw' U2 Rw' U' R' U2 R U Rw' (25) | Flips UF,UL,UB, shoots DFR to UFR |

Rw' U R U2 R' U' Rw' U2 Rw' U2 Rw' U' R U2 R' U' R U' R' U' Rw' (25) | Flips UF,UR,UB, shoots DBR to RFU |