For rape, if reported within 1 year of the crime the SOL is 10 years (or, if victim is under 14 years old, until the victim's 28th birthday). If not reported within 1 year, then the SOL is 3 years (or, if victim is under 14, 3 years after victim turns 18, but not more than 7 years after the rape).
Domestic violence is not a specific crime, but rather a "tag" that can be attached to (almost) any crime if committed against a "family or household member." So the SOL would vary depending on the crime. Generally, there is no SOL for homicide, SOL is 10 years for sexual assault (or until the victim's 28th birthday if the victim is under age 14 at the time of the crime), 3 years for most other felonies, 2 for gross misdemeanors (the vast majority of domestic violence assaults will fall in this category) and 1 for misdemeanors.