I found multi-blade razors and shave oil to be a really bad combination. You spend more time de-clogging the razor than actually shaving.
+1. Tried it, but found the cut stubbles clings to the oil and clogs the razor up.
OP, I would try a brush & shaving soap. Body Shop do a half decent brush & shaving soap; macca root something or other in a blue tub. It’s about £8, but lasts ages.
Also, grow a bit of stubble and take 5 mins looking at which direction all the hairs are growing. You might need to alter the direction you shave in certain areas of your face, depending on which way the hairs grow.
Do you use the hottest water you can stand without scalding yourself? I find if the water isn’t proper hot, I always nick myself.
Oh, and finally perhaps try shaving with a little less pressure on the razor; you shouldn’t be cutting yourself at all with a cartridge razor.