General annoyance or frustration:
* Annoyed
* Irritated
* Frustrated
* Aggravated
* Disgruntled
* Upset
* Troubled
* Displeased
* Distressed
More serious or intense:
* Tormented
* Harassed
* Perplexed
* Puzzled
* Confused
* Bewildered
* Baffled
* Troubled
More formal:
* Irritable
* Cross
* Peevish
* Impatient
More specific:
* If referring to a problem or issue: Difficult, problematic, challenging, intractable, knotty
* If referring to a person: Fretful, moody, irritable, short-tempered
The best synonym for "vexed" will depend on the specific meaning you want to convey.