Effects of Neodymium magnets on PCB
None of the listed parts are sensitive to magnetic fields, so the mere presence of the magnet shouldn't bother them at all.

The sensors and magnets will be physically attached to the box, and so must move together.  To induce current, the conductor and the magnet must move at different speeds.  Since they are all attached to the box, all the parts will be subject to the same motion - no induced current, no problem.



The LSM6DS3 has provision to connect an external magnetometer, but you don't mention having one in your project.  If you do have a magnetometer attached, things get more complicated.  Probably better to use suction cups for mounting the box in that case.

Vibration could cause some low currents to be induced in your traces and wiring.  Vibration can do this because the parts aren't perfectly rigidly attached to the box and will therefore move a tiny bit in relation to each other.

That shouldn't be enough to bother any of the circuits you mentioned.

The wooden box will have pretty much no noticeable effect on the magnetic field.  About all it gives you is a little more distance from the magnet - which by itself reduces the strength of the field when it reaches your parts.  But, the wood itself doesn't really matter - it might as well be air for all the difference it would make.