Nausea is a common gastrointestinal side effect across many antidepressants that affect serotonin activity, since serotonin receptors are present throughout the gut. Taking trazodone with food can both reduce nausea and change its absorption profile slightly.
Vomiting is less common than nausea alone but is listed in trazodone's overdose reaction profile as well, so vomiting that is severe, persistent, or accompanied by other symptoms warrants medical attention.