Is there a grammatical term for moving a word to the front or back of a sentence?

Moving an element to the front of a clause (often in order to emphasise it) is, quite logically, called fronting.

This is different from inversion (as mentioned in tchrist’s answer) in that inversion usually is not optionally chosen for emphasis, but a mandatory part of various syntactic processes. Questions, for example, normally require subject-auxiliary inversion, as do certain fronted adverbs.

That's not to say the two are entirely unrelated, though. In fact, it used to be that fronting and inversion were quite closely related phenomena: the verb in Germanic languages like English historically tended to like being in second position (the word order is SVO), and in order to keep the verb in that position when fronting some non-subject element, the subject would have to be moved to a position after the verb—in other words, the subject and the verb were inverted. Very frequently, the fronted element would be an object, but it could be just about anything.

In most other Germanic languages, inversion is still the rule when fronting elements, but English has (perhaps under influence from French which employs inversion in a very limited way) gradually abandoned the system: in current English, it is more common for fronted elements to simply be considered outside the clause itself and often set off by a comma. The clause itself can then retain its regular word order.

To give a few examples (word order in parentheses; A is ‘adverbial’; fronted element italicised):

I saw Jane yesterday (SVOA).
Yesterday, I saw Jane (ASVO).
Jane I saw yesterday (OSVA).

In languages like German or Swedish (or indeed some older stages of English), these would be:

I saw Jane yesterday (SVOA).
Yesterday saw I Jane (AVSO).
Jane saw I yesterday (OVSA).

– but of course that doesn't work in current English. For an English example, you have to go back in time, for example to William Shakespeare:

Tybalt: Romeo, the hate I bear thee can afford no better term than this: thou art a villain!
Romeo: […] Villain am I none; therefore, farewell. I see thou know’st me not.
_{Romeo and Juliet, Act III, scene I}

Here the subject predicate villain is fronted to the start of the sentence, with subsequent inversion of the subject and the verb.

What hasn't changed in modern English is that elements can be emphasised by moving them to the head (front) of their clause, that is, by fronting them.

Unlike Arabic, though, moving an element to the end of a clause is not a tactic used for emphasising in English; I am not aware of any word for that.

When the verb precedes the subject in English, this is properly called inversion of the normal state of affairs. English has two main sorts, subject–verb inversion and the related subject–auxiliary inversion.

Subject–verb inversion

So given an SV (subject–verb) sentence, rendering that as a VS (verb–subject) counts as classic subject–verb inversion. This happens in a broad variety variety of contexts, of which these are merely some common cases:

• Is he still here? [questions]
• Neither am I. [negatives]
• Around the corner came the screaming fire engine. [adverbial start]

Subject–auxiliary inversion

As something of a sub-category of this, when you have a compound verb like do think or is running or won’t see or could have run, you invert only the first element of the verb.

• Does he really think so?
• Is he running late?
• Won’t he see her already?
• Could he have run any faster?

This are all cases of subject–auxiliary inversion. Notice that contractions like won’t or can’t count as auxiliaries in their own right for these purposes. If they had not been contracted, you could not move the negative part:

• Will he not see her already?

Other orderings beyond inversion

However, English also has plenty of other syntactic variation that is not considered inversion. For example, you can change an SVO sentence to OSV for emphasis:

• Helms too they chose, and round shields: [...]

Some people loosely refer to any ordering change as “inversion”, but linguists seem to restrict it to SV becomes VS only. So for them, this is not (“technically”?) considered inversion because you aren’t swapping the order of the S and the V: they stay in the same place, and you front the object to the very beginning of the sentence to give it special emphasis. This we also do from time to time.

Historically English also had an SOV ordering, but that now sounds archaic or perhaps poetic. Here is one with straight SOV:

• With this ring, I thee wed.

And here is one where the object is moved to the middle of the compound verb do part so that it comes before the main verb but after the auxiliary:

• Till death do us part.

No English speech community that I know of still uses SOV in their “normal” speech these days, but you still may find it in deliberately archaizing literary contexts, including poetry.