M can be done fast in a a ton of different ways. Just find a way that you like and do that. Or use whatever works best for the position your fingers are in at that time.
As for EO, I only need to check the U layer stickers and FD sticker. On the U layer, the edges that are oriented have U/D (W or Y for me) on top. If it's not U or D color, it's misoriented. FD should not be a U or D color. If it is, then it is also misoriented. Since edges are always oriented in pairs of 2, you can deduce whether or not DB is oriented. Here's a few examples:
M U' M U2 M2 U' M' U2 M' U2 M' U' M2 U2 M U M' U M2 U M2 U2 M U' M'
First do an M' to fix centers.
U layer - Only UL has U/D color on top, so the other three are misoriented (UB, UR, UF). I look at FD. It is a U/D color, so it is misoriented. That makes 4 misoriented edges, so I know that DB is correct. U M' U' M to orient
U2 M2 U' M2 U2 M2 U2 M' U2 M U' M U2 M2 U M' U' M2 U' M' U2 M U2 M' U'
M to fix centers (else we get the mirror of what we had last time - boring)
U layer - UR and UF have U/D colors, so they are correct. UB and UL do not, so they need to be flipped. FD is a U/D color, so it is misoriented as well. That's only 3 wrong edges though, so I know that DB is misoriented also. M2 U' M' U' M'
U2 M2 U2 M' U2 M' U' M U M U M U' M2 U M2 U M' U2 M2 U' M2 U2 M U2
M' to fix centers
U layer - UR and UL do not have U/D colors, so misoriented. Look at FD - U/D color => Misoriented. That's only 3 edges, so DB is also misoriented. M' U2 M' U2 M U' M (plus paired up UL/UR! Aren't you guys proud of that LSE? I've never intentionally done that before without having to do extra thinking!)