I can imagine there are several different ways to measure angle of attack (accelerometers, relative pressure measurements between pitot tubes, etc), but I'm curious which sensors the 737 MAX uses for its MCAS system since it's been in the news recently.
The pitot tube has nothing to do with the angle of attack. It is used for measuring pressure which in turn gives you the airspeed.
Accelerometers are used for the Inertial Navigation System.
The angle of attack is another sensor (shown below): the principle is that it rotates and reads the angle between the current position and the reference position.
Regarding the 737 MAX, there are two AoA sensors one on the captain side and one on the first officer side.
The MCAS reads the AoA from the captain side.
I think you are talking about the heavy MCAS "corrections" that led to the two crashes. The MCAS is part of the STS (Speed Trim System). Apart from the Angle of Attack sensor, MCAS also checks that the flaps are up (retracted) and the auto pilot is off before it triggers the heavy nose-down trim. Some sources add that MCAS also needs a high bank angle and the engine at high power before it activates.
BTW the MCAS does not check to see if the AoA sensor readings make sense. It accepts the sensor readings blindly.