Semicolons are easy; they just join related sentences. A semicolon joins two complete sentences and show a closer relationship than using a full stop. They substitute for fragments like 'therefore,' 'that means,' and 'for example'.
Also, I think you can use them to seperate lists of items where the items themselves contain commas; The winners are from Bethlehem, PA; Syracuse, New York; Los Angeles, California and Little Rock, Arkansas.
Both parentheses and em-dashes are a little suspect. They can suggest a rewrite; often you have embedded one idea inside another, and you're better off placing the two ideas adjascent. Or just use commas for simple parenthetic expressions. "The dog took the treat (half-chewed and slimy with saliva) and placed it in my lap," is better written "The dog took the treat, half-chewed and slimy with saliva, and placed it in my lap."
Anyway, I'm 3,000 miles from my copy of Strunk and White, so I could be wrong...