Hey guys, so I've had a skewb and a master skewb, as well as a face turning octahedron for several months now, and I can't figure any of them out intuitively. I've accidentally solved the skewb once, but I have no idea how.
This takes quite a different line of thinking than the cubes/cuboids and helicopter cube I'm used to.

Are there any tips you guys have for me or simple/semi-intuitive algorithms I could use? I don't want to memorize algorithms for these like I did for the 3x3x3 unless it's just for a parity or something, but I just can't figure out what to do.

The skewb, I find, has two main lines of logic for solving: the first is to solve a "layer" (what you turn), which is half of the puzzle at once. You solve this intuitively, then algorithms for the rest. The method that I use is not my own, but it works well. Start by putting the white or other colour corners of one face with their respective centre. This is intuitive. Then, use algorithms to solve the final centres and corners. The algorithms for the corners is something like (B'/A/B/A'/)*2 where A and B are adjacent corners on the right and A denotes a corner turn in the clockwise direction of the corner to the top-right-back. For the centres, you have (B'/A'/B/A), then turn the whole puzzle 90 degrees to the right on the Y-Axis, then perform (C/D/C'/D') where C and D are the adjacent corners on the left side once the puzzle is turned. That rotates 3 centres counterclockwise (not sure which 3, I think that it's the L, F, and D though)