I'm sure there's never been done an experimental study of the emotional impact, measured through skin conductance or through a simple questionnaire (similar to what produced this), of each of these words. Maybe one could extract a word2vec embedding and then compare cosine distances and directions on relevant dimensions. I think you'll have to rely on a qualitative comparison possibly but not necessarily backed up by dictionaries, which may or may not provide enough nuance to distinguish what native speakers do very successfully. Also, there's a lot of overlap.
For the logical concept of 'expressed in few words', there are a number of synonyms (I'm sure there are many more):
They all to some extent provide a nuance that is different in some direction that could easily be explained with more words and would help distinguish.
But at a first pass, one could place them on a continuum of rudeness; there would surely be some overlap between neighboring ones but more sure of the difference towards the ends.
For example, 'terse' is not rude at all, but 'brusque' is. 'Blunt' is surely a shorter message, but also has the primary meaning that it is too honest. 'Curt', from the French for 'short', is slightly rude but doesn't have the connotation of too much honesty, just short.
All the following are the canonical entries (for comparison) from the OED:
blunt - 5. Abrupt of speech or manner; plain-spoken; curt; without delicacy; unceremonious.
brusque - 2. Somewhat rough or rude in manner; blunt, ‘offhand’.
curt - 2. a. Of words, sentences, style, etc.: Concise, brief, condensed, terse; short to a fault.
terse - 3. spec. Freed from verbal redundancy; neatly concise; compact and pithy in style or language.
As you may well be aware, there are no exact synonyms. If a word is differently spelled, it has -some- difference. It may be negligeable, and it may lead to semantic drift or even swapping of meaning (viz. uninterested and disinterested). Just because some of the above definitions use another word in the list doesn't mean they are replaceable in the exact same circumstances and lead to the same communication. From just the dictionary entries of blunt and curt, I'm failing to distinguish them, even though I know it is not written there that blunt is much more evocative of something physical (it could be used of an object), where as you can't apply 'curt' to objects, only utterances.
So if forced to answer on the rudeness-politeness scale, terse is neutral, and curt, brusque, and blunt are roughly all 1/2 way to rude with a wide spread depending on context. Much of the latters' rudeness is from context and not so much inherently in the word itself. They are not equally all the same distribution.