Learn English – the nominal form of the verb “to give”

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.

In short, your only option seems to be exegese (or possibly exegeze, but probably not), if you must have a verb that would be acceptable to the OED.

But it should be noted that, for what is probably the majority of words on -sis, no verb is ever used; perhaps recasting your sentence would be a better idea, e.g. she interpreted the passage. Using the Greek infinitive exegeisthai is a bad idea that will send classicists off screaming.

The only traditional way of forming a verb based on a Greek word on -sis that I am aware of is -se:

Parenthesis => parenthese

Diagnosis => diagnose

Paralysis => paralyse

Basis/-se => base

Metamorphosis => metamorphose

Occasionally, modern forms on -sise are created, as in those based on -thesis (hypothesise, synthesise); I can't think of any other example. Those few Greek words on -sis whose noun-equivalents already end on -se in English also use -se for the verb, as in phrase and base.

For forms on -ise and -yse, you may encounter -ize and -yze in America, respectively, and possibly sometimes elsewhere too, so exegeze may be considered a valid alternative depending on your local tradition. However, this strictly has nothing to do with the formation of an English word based on Greek, but rather on regional variations within English. Lastly, I do not believe Americans normally do this with words on -ese/-eze (they stick with -ese: only after -i- and -y- is this z commonly used), but that's your call.

Your examples ostracize and baptize are different, because they have somehow retained or regained the z that was originally there in Greek (ostrakizein, baptizein), as opposed to in exegeisthai and most other verbs. The same applies to apologize/apologizein. This confusion is the reason (most?) British publishers and style books use -ise/-yse for verbs based on Greek nouns on -sis (Oxford and Cambridge alike, I think), like analyse; but they do often do use -ize for other Greek verbs, like baptize, and for words taken from non-Greek stems, like immunize, realize, colonize (either Oxford or Cambridge—I forgot). They usually do not, however, use -yze where Greek had no -uzein (so practically never). I know, it is a bit tiresome having to remember the exact origin of such words—I am usually too lazy to do so, I must confess.

The -i- in *exegise/exegize is not really defensible, because that is normally not done with words derived from -esis, but only with those derived from -isis. The -ize in energize comes from Greek -(e)izein, as energy comes from energ(e)ia; the -i- in apologize from Greek -izein as in apology, from apologia. The -y in English represents -(e)ia in most Greek (and Latin) words, and hence nouns on -y in English have verbs on -ise/ize.