What obeys status effects and what doesn't isn't really documented anywhere, so I made a simple chart of what obeys what.
If a thing obeys slow, it gets reduced by whatever slow% the unit has; for reclaim it means it gets disabled when the unit is partially reclaimed, and for EMP/disarm it means it gets disabled as long as the unit has over 100% in either of those.
Obedience is green, resistance is red, yellow is "depends" - see explanations below.
DSR is Disarm, RCL is partial reclaim.

1) Windgens disobey slow, everything else obeys.
2) Animation includes deployment (Slasher, Crabe, Djinn beacon placement) and is per-unit -- most units disobey.
3) Non-combat Morph cleanses EMP on use and grants EMP immunity as long as it's active (but cannot be activated if already EMPed).
4) Reclaimed units cannot be picked up but units already being transported can be reclaimed.
5) Teleporting is only disabled by EMP/Disarm when Djinn or Lamp are stunned, not the passenger.
6) Only dedicated sensors obey (ie. a Conjurer's jammer or a Reef's radar will stay). The dedicated sensors are Sneaky Peet, Eraser, both Radar Towers, Sonar Station, and Vulture.
Now here's some values related to status effects.
The decay rate is 2.5%/s for EMP and Disarm and happens constantly.
For slow, the decay is 4%/s but gets stopped for 0.5s upon refreshment.
The shield damage conversion ratio is 1/3.
They are ownerless.
Status effects obey armor and work upon current health value.
Max Slow is 50% but it works at whatever % it currently is at; EMP and Disarm only work when over 100% and how high they can go depends on the weapon.
Capture decays at 4%/s without stopping, ignores shields, ignores armor, is separate for every alliance, works on cost instead of health and gets scaled with health in a weird way: the multiplier is x(3 - 2*HP/maxHP).