Your armature should be at the top of the modifier stack. And it’s pretty odd that the objects are rotated -90 degrees on the x axis.
The mesh stretching when you rotate anything happens because you’ve got a scale on your armature in object mode that isn’t 1 1 1. To fix this, first clear all the parents by selecting everything with a a, then press alt p. Next, set the scale of the armature to 1 1 1 in object mode, you’ll only need to change one value.
After that, set the 3d cursor to be at the object origin (the orange dot), set the pivot point to 3d cursor and scale in edit mode on the y axis until it fits the mesh. Then add armature modifiers to the objects that should have them (and put the modifiers at the top) and parent everything else to whatever it should be parented to.