Otdfbt

I started to learn orchestral music with four part harmony for choirs and there you always try to avoid parallel fifths and octaves...
How does this relate to a whole orchestra? Do you have to take care of them only within the sections (strings, brass, woodwinds), do you have to take care of them within the whole orchestra or does it even matter in the whole orchestra?

IF you care about avoiding parallel fifths and octaves—and that’s entirely a stylistic choice on the part of the composer—then, for the most part, you care about them regardless of the instruments involved. And you care about them at the level of basic harmonic structure completely independent of the orchestration of the moment. In other words: no, it isn’t something you avoid only within a particular instrument family, it’s orchestra-wide.

For the European composers of common-practice tonal music in the 18th century (with considerable overlap into the 17th and 19th centuries as well), they almost always avoided these parallels, and they did so regardless of whether it was a piano sonata, or a symphony or anything in between. It’s a fundamental aspect of harmonic connection for them, not a surface level concern. What I mean is: by the time they’re thinking about how to distribute the harmonies amongst the instruments, the voice leading is already set. It’s not even something a composer of that period had to consciously think about, it’s just how the primary musical grammar worked for them. When they did want the sound of parallel fifths—as Beethoven did in a famous passage of the sixth symphony—they wrote it, but it wasn’t the default.

Here in the 21st century, most of us don’t already have this preconceived idea about how harmonies “should” connect. A lot of popular music styles use parallels all the time; in a lot of basic heavy metal music I would (only half-facetiously) say a composer was making a mistake if they didn’t use parallel fifths and octaves. Different musics have different grammars, but those grammars tend to apply regardless of specific instrumentation.

Parallel 5ths are absolutely fine in choral music. In fact, the very earliest choral music was ALL parallel 5ths! Where they AREN'T fine is in a style of writing which values the effect of four independent voices, the style epitomised by Bach's chorale settings. Listen to the beautiful rich harmony of those, also listen to the barer but still beautiful effect in this piece.

Both styles are perfectly valid in orchestral writing.

To address your question more narrowly:
There is a principle in orchestral writing that in a tutti the harmony should be complete within each section - i.e. you don't give the root of a chord to the strings, the 3rd to the brass and the 5th to the woodwind. If you follow this principle, it implies that any parallels WILL arise both within and between sections.

There is a similar question to this one here: Parallel Fifth in a Symphony Orchestral

However, I wouldn't say that it matters too much within the whole orchestra. People these days are so familiar with the sound from all the pop & rock songs out there. I think it will just fly by within a whole orchestral score with so many instruments playing at the same time.

If you compose something and then think "ohh boy, this sounds like block-chords", then you probably should change it, but otherwise - if it sounds good to you, it sounds good to other people as well.

You probably should only take care of them in small arrangements when they're exposed, but even then... There are no rules in music. If you like the sound, then stick with it.

Two instruments which play parallel fifths or octaves will often sound like a single more powerful instrument. The extent to which this occurs will generally depend on the particular instruments involved. This effect can be very useful if employed in places where it would make musical sense. It can also be jarring if it occurs willy-nilly without rhyme or reason.

Note that in a symphony orchestra, the number of different instruments will typically be much greater than the number of different musical lines that be maintained simultaneously. The most useful way to employ a symphony orchestra will thus often be to have various groups of instruments play various sections of music in parallel octaves or, less commonly, fifths, so that they sound--for those sections of music--like unified more powerful instruments. Note that when using parallel fifths, the part that's up a fifth should generally played on an instrument with a relatively "pure" tone, such as a flute.

Different musical styles are more or less permissive of parallel fifths and octaves, and this can vary even between pieces by the same composer.

However, there is no fundamental difference between orchestral writing and choral writing from this perspective. If you wanted to write an orchestral piece using the same musical language that you've used for choral music, then you would avoid parallels in just the same way.

One difference is that an orchestra has many more instruments. This doesn't mean you need to attempt to write 50-part harmony! typically, not all the instruments will be playing at once, and if they are, it is common to have multiple instruments playing the same part . It may appear that there are parallel unisons or octaves between these instruments, but if two parts are playing exactly the same music (even an octave apart), then this is called doubling, and is not an example of parallels.

Often, orchestral music will be based around some fairly simple (4-6 part) harmony. This underlying harmony will obey the normal rules for the style (including avoiding parallels if appropriate), but the parts might be blended and embellished in different ways among different instruments for textural reasons. This is called orchestration, and it's a separate skill that is not so important in choral music.

This answer affirms the need to specify genre, but specifically explores upon the differences in parallel 5ths and 8ths for 4-part writing versus orchestral writing in 18th-century music.

The purpose of avoiding parallel 5ths and 8ths, especially around 18th-century music, is to give the listener the impression of distinct musical lines, especially in the diatonic setting. Parallel 5ths and 8ths would otherwise blur the two lines together. If your goal is to utilize this effect of distinct melodic lines, then you would use it in the same way with the orchestra as you would do in 4-part harmony. Obviously, if you instead want some sweeping parallel 5ths and octaves to intensify the piece, by all means, do so. You are the composer, after all.

In terms of 18th-century composition: now, there's a catch, a key difference between 4-part harmony and orchestral writing. The orchestra is much bigger. In this case, octave doublings, are allowed, but they are different from parallel octaves.

Octave doublings result when a whole line is played in octaves by multiple instruments for the purpose of increasing dynamics, strengthening the line, diversifying timbre, etc. Note that this is still one line played by multiple instruments. One establishes the 2+ instruments as playing the same line from the start, and they play octaves for the duration of the line. This is distinct from parallel octaves, where two already-distinct lines briefly "merge" with parallel octaves, giving a feel of two lines collapsing into one.

In 18th-century music, 5ths moving in parallel motion are not allowed in any context, except in an unrelated topic of German 6ths.