In my school's projectors, I wonder what kind of lamp are inside of them. are the MH, UHP MV, or Xenon short arc?

Generally modern LCD projectors use UHP mercury vapour lamps.  Some of the earlier ones used metal halide lamps though, and conventional overhead projectors usually used halogen incandescents.

This is an example of one of the metal halide examples from my projector.

http://www.lighting-gallery.net/gallery/displayimage.php?album=1911&pos=0&pid=56579

Overhead projectors used halogen incandescents and later ones the MH, video projectors MH and UHP.
Only cinema theater projectors are using Xe. The problem with Xe is, then for lower power the intensity is not as high as with the UHP or MH, while the big cinema need the intensity and power levels only attainable with the Xe.
The only place I've seen the lower wattage Xe's are the medical light engines, as the Xe lamps do not pollute the area (lamp cooling exhaust) when they explode or leak, so their use is made easier (no complications with the protection against Hg poisonning). But the cost is the power input: The task, where 100W UHP is way enough require at least 250W Xe, with related thermal management troubles.

I've never seen overhead projectors using metal halide.
But the halogen lamps they use are 82 volts.

Meopta used 24V 500W halogens and in late 80's and early 90's (before they stop with them) with 150W MH.
Then I remember some were converted to 250W MH to work with special LCD screens as computer projectors (about mid 90's)

Thee were external LCD screens (LCD in a transparent frame) made as a complete device exactly for this - to place them on OHPs. This worked but not too well, given th low contrast of LCD's of the time to begin with (or was that just the model they used in my school so bad ?). You can make better projector from an OHP and a modern LCD panel