Your pain dictates your exercise/activity selection.
Why this matters:
Stretching and strengthening are two common forms of exercise when rehabbing from sciatica pain. Lengthen the piriformis, strengthen the glutes and abs. Each technique has a specific time and place. Improper use of either will result in no results or worse, more pain.
Strengthening muscles is great for when pain is present with movement. Example: pain with walking or pain with doing the squat. This indicates that specific muscles need to be activated to do that activity without pain.
Stretching muscles or joints is fantastic for pain present at rest. That means, if even sitting still causes pain, we need to find out which muscles are tight/overactive to relieve that pressure.
If you have pain mostly at rest, focus on stretching. Every stretch that you do should be directed at relieving your pain.
If you have pain mostly during movement, focus on strengthening. Build the muscles that allow you to do the activities that you love with less pain.
Managing this pain can be simple. Avoid being confused with super complex principles and plans. Your relief is priority before anything else.