What is the right verb for "measurement"?

Most commonly we say to "take a measurement", "make a measurement", or simply to "measure". Either can come in all the different tenses. "Please take some measurements of the temperature." "Yesterday I measured my room so I'd know how much paint to buy." "We will make some measurements of the energy released during the experiment tomorrow."

I don't think I've ever heard a native speaker use any of the other options you give. Maybe in the right context any of them could be valid, but they certainly wouldn't be conventional.

Instead of saying "Take a measuremement of length/temperature/whatever", we often just say "take the temperature", "take the height", etc.

Meauring weight is special: You don't usually say, "We measured the weight of the box", you say, "We weighed the box". I can't think of any other measures like that. No one says, "We lengthed the height" or "We temperatured the liquid". Sometimes we talk about "clocking the speed" rather than "measuring the speed", especially when talking about the speed of a vehicle.

Taking sounds best to my ear. And yes, the measurement has been taken is the passive form.

Alternate forms:

• I took the measurement this morning.
• We should have measured this couch before attempting to move it.
• I cannot measure this without outside calipers.
• She is measuring the flour for the cookies.