Those these seem to come up all the time, for the most part I'm unclear as to how to differentiate them. Per the title, what are the subtleties in use and meaning between: 特殊, 格段, 特段, 特別, and 別段?
In daily language, 特別 is the word with broadest meaning that is approximately same range as English special. 特別 can replace any other word you've mentioned in most settings (unless there's predefined terminology), only with possibly less exact and/or apposite feeling.
特殊 suggests that something belongs to a rarer type/class rather than one-off uniqueness. The word carries an overtone that you're trying to categorize it. The word also sometimes stands for euphemism of unlaudable quirkiness.
格段 means either:
燃費が格段に向上した。 Its fuel efficiency has greatly improved.
特段 and 別段 specifically refer to that treatment or consideration is special. You can read the 段 as "case", so that they mean "of special case" and "of separate case". 特段 sounds like needing more carefulness than 別段. It should be noted that they may be more seen as a part of idiom "not particularly".
（特段／別段）の定めがない限り unless otherwise specified
（特段／別段／特別）異状は見当たらなかった。 I found nothing particularly unusual.
特異: peculiar, singular
別格: in a class by its own
特殊, 格段, 特段, 特別, and 別段
I think my previous answer was inadequate, so I carefully examined various materials and dictionaries and thought about the answer, but by this answer I thought I could not solve the questioner's problem and I decided to stop the work.
After that, I thought about the way to explain subtle differences between the five words of similar meanings given by the questioner to those who are not Japanese native who are studying Japanese.
First, I looked up the meaning of five words in an English dictionary and Japanese dictionaries. From the meanings of Japanese dictionaries and example sentences, I could understand the difference between the five words in Japanese. However, it is almost impossible to distinguish between the meanings of each other from the meanings in English. Every word has the meaning of "special". I could understand the reason that the questioner wanted to know the subtle difference in meanings between them.
I thought about how to grasp the difference between these words if we are Japanese.
First of all, we first check the sound by looking at these words. Next, we suppose some possible words from the sound, then narrow down the words by looking at the kanjis of each word.
As an answer to the questioner, I thought, the analogy of narrowing down the possible words by the kajis is effective.
All five words given are made up of two kanjis. If I separate all the kanjis constituting the five words apart, I could get five different kanjis. Combining the five kanjis by 2 characters gives a total of 20 different words. Of these words, 13 are meaningless combinations, and only 7 are left as meaningful words. The questioner found out five of the seven meaningful words.
First, I looked up the meanings of five individual kanjis in a kanji dictionary. Next I looked up the composition of the kanjis of seven words and gave it a drawing shown below. Since all the words have the meaning of "special", I named the title of the drawing "Members of the Special family". Next I imagined the meaning of each of the seven words from the meaning of the kanjis constituting each word and wrote them in the drawing. Lastly I added the meanings in English that I looked up in the dictionary before.
From the meanings in English it is difficult to distinguish between the meanings of the words of each other, but from the meanings I imagined, the meaning of the nuance may be felt a little by native Japanese as me.
Although the result is not sufficient, I felt that such a probing method may be meaningful for knowing the similar words' differences.
Here is a table of the synonyms of 「特別」 classified according to the meaning. If you have enough time, you could know which word is used well by checking the frequency of each word on the Internet.
特別 879,000,000 hits
格段 21,700,000 hits
格別 16,400,000 hits
特殊 622,000,000 hits