Harold Wentworth & Stuart Flexner, Dictionary of American Slang, first edition (1960) has this entry for pissed off:
pissed off {taboo} Angry; enraged; disgusted; completely and thoroughly exhausted; fed up; unhappy; forlorn. One of several such terms very widely used by Armed Forces in W.W.II and carried into civilian life afterward. Though still taboo, this term has passed into sophisticated use among the culturally elite or pseudo-elite.
This edition of Wentworth & Flexner has no entry for pissed in the sense of drunk.
Robert Chapman & Barbara Kipfer, Dictionary of American Slang, third edition (1995) shows some evolution in the variant wordings used:
pissed off adj phr (Variations: pissed or p'd or peed off or po'd) Angry; profoundly annoyed; indignant: [examples omitted]
This edition of Chapman & Kipfer has no entry for pissed in the sense of drunk, either.
I remember that people began shortening pissed off to pissed (still with the meaning "angry") during the middle 1970s, because I had a roommate in college at that time who used to counsel anyone who confessed to being "pissed off" that "It's better to be pissed off than pissed on." He told me that the truncated form pissed had ruined the fine edge of his wise saying.
On the other side of the Atlantic, Eric Partridge, Dictionary of Slang and Unconventional English, first edition (1937) reports a very different meaning of piss off:
piss off. To depart, esp. to depart quickly : low : late C. 19–20.
And for "pissed," the same edition of Partridge has this:
pissed or pissed-up. (Very) drunk : low, and military : C. 20.
As of the fifth edition of Partridge (1961), the dictionary still had no entry for pissed or pissed off in the sense of "angry." However the eighth edition (1984) has these additions:
piss off, v.i. To depart, esp. to depart quickly (often as an imperative: piss off!, go away!): low: late C.19–20. ... —2. V.t. To irritate, annoy, often with connotation of either malaise or disgust: since late 1940s. [Example omitted.] Hence pissed off.
...
pissed off. Disgruntled, 'fed up'; very much displeased (with someone or something): since late 1940s, Services; in 1970s very common among students.
It thus appears that U.S. English slang and British English slang ran on separate tracks for a long time, but that both now acknowledge and use the "angry" sense of pissed off. Further, I'm quite familiar (conversationally) with pissed in the sense of "drunk," so that meaning of the term must have become at least somewhat naturalized in parts of the United States in the past two decades.
Here's Eric Partridge from the Dict. of Slang and Unconv. English:
sod. A sodomist: low coll.: Mid-C. 19-20; ob.-2. Hence, a pejorative,
orig. and gen. violent: late C. 19-20.
Often used in ignorance of its origin:
cf. bugger.
So your sense of "sod" is on the money. Suffixial "off" marks a general epithet as an insult, as seen in "piss off," "f-ck off," "bugger off," etc., all used in the manner of "please go away." Also note that "sod" in this sense is UK usage only. In US English it only refers to topsoil and turf grass.
Best Answer
In Britain 'to knock off [work]' is a perfectly normal and innocent thing to say. It is informal so you might more often hear 'to finish work' or 'to leave work'.
I've never heard it used to mean 'masturbate'.
In Britain someone might say 'to knock one out' to mean masturbate but the addition of the words 'one' and 'out' makes the verb completely different.