***** NOT A TEACHER *****
Here are some ideas from various experts. I have emphasized certain words by underlining them.
(1) "An old ... prefix, not referring to an act as a whole, but only to the beginning or end: She arose (rose up); They abided by their beliefs (remained faithful to the end); She awoke (became awake).
Sources: Dictionary.com
The Random House College Dictionary (1982).
(2) "By the use of the prefix, the meaning of ["rise"] becomes more intensified." / "Today "rise" has almost supplanted the use of the verb "arise." / "Arise" usually combines with negative words: "Misunderstandings sometimes arose between judge and counsel [lawyer]."
Source: (A)rise and (A)wake / An Investigation of Two Verb Pairs by Alexander Lakaw. (His dissertation is on the Web)
(3) Some people suggest that "rouse" is more often used literally: "Once roused [or "aroused'], nobody could go back to sleep." Some people suggest that "arouse" is more figurative: We aroused [or "roused"] the neighbors. [My note: Be careful of the verb "arouse." Sometimes it refers to romantic feelings. The forum rules are very strict, so I cannot explain further.]
Source: The Columbia Guide to Standard American English by Kenneth G. Wilson (1993). Columbia University Press of New York.
(4) "Wake" is the common, everyday word: "Wake me at seven" and "The fire engines woke [up] the baby." / "Awake" is used in poetic senses: He will awake no more." [My note: I guess that means he is dead.] / "Awake" is also figurative. [Here is an example from the Web: "The medical profession is awaking to its social responsibility in ...."]
Source: Dos, Dont's & Maybes of English Usage (1977) by Theodore M. Bernstein with the assistance of Marylea Meyersohn and Bertram Lippman.
(5) In "arise," "arouse," and "awake," the "force of this prefix naturally becomes merely intensive."
Source: A Higher English Grammar (1891) by Alexander Bain. Google eBook
(6) In "arise," "arouse," await," "awake," etc., the "meaning has become vague [not clear], but seems in some words to be initiative [to start], in others intensitive, and in "a-rise" the "a" apparently = "up."
Source: English Grammar, Historical and Analytical (1878) by Joseph Gostwick. Google eBook.
(7) One expert says that the "a" in words such as "arise," "arouse," "abide," "await," "awake," etc. expresses "more or less of additional expressiveness." [My note: Today, one might say "I am weary [tired] of life." This expert says that Shakespeare used the word "aweary," which gives "additional expressiveness" or emotion. I do not think that we use "aweary" today in regular speech.]
Source: The English of Shakespeare (1888) by George Lillie Craik and William James Rolfe. Google eBook.