Is the SVOMPT word order necessary in creating a sentence?

I learned the English word order SVOMPT (Subject, Verb, Objects, Manner, Place, Time) rule at school. Although it was a quite straightforward rule when I was studying, now (under more influence from Slavic languages) I find myself not obeying it sometimes.

So far, I haven't noticed that others do not understand what I say, but that could be because most of the people I speak English with are also from the Slavic language group.

We usually put the most important part (the one we want to emphasise) at the end in Slavic languages. Also, the word order is quite relaxed in general. How about English?

Is a sentence where one does not apply the SVOMPT rule easily understandable for an English native speaker?

I found this page on A guide to learn English which deals with direct and indirect objects. Is word order switching also common in other cases?

Answer

Word order is very important in English because it is so lightly inflected.

The core SVO sequence is usually obligatory in declarative sentences, and there are fixed transformations for negatives and interrogatives.

But your MPT pieces are 'Adjuncts' - not part of the core sequence - and may move around. Moves to the front of the sentence are common:

I bought a boat last summer. ... Last summer I bought a boat.
We take taxis a lot in New York. ... In New York we take taxis a lot.
He finished the job as quickly as he could. ... As quickly as he could, he finished the job.

And a 'light' Adjunct (one of few words) may sometimes be moved to the inside of the core sequence:

I quickly polished off the sandwiches.

Note that "^✲I polished off quickly the sandwiches" is not acceptable (although as Russell Borogove points out, it's perfectly understandable). However, a light adjunct may occupy that position if the Object is markedly heavier:

We found to our dismay that he had already started working.

Such intrusions are often set off with pauses in speech, and commas in writing:

We found, to our dismay, that he had already started working.

ADDED:

As far as emphasis goes, we tend in English to rely more on vocal stress than on sentence position; position is more likely to be determined by contextual rhythm, what the previous sentence was or the previous speaker said. In both writing and we speech we also have 'information packaging' strategies that throw the focus of the sentence onto a specific piece of information: It was last summer that I bought a boat. What I bought last summer was a boat.

It's a very complicated subject about which many fat books have been written. By and large, if you keep your SVO together, your listeners will figure out what you mean pretty easily.