Bring first 5 ingredients to a boil in a small saucepan over medium-high heat; reduce heat to low, and simmer, stirring occasionally, 5 minutes. Add jalapeño, and simmer, stirring occasionally, 5 minutes. Remove from heat, and let stand 30 minutes. Stir in lime juice.
Stir together strawberries and next 4 ingredients in a medium bowl. Add vinegar mixture, and stir to coat. Serve immediately, or refrigerate in an airtight container up to 2 days.