Translation:František and Matěj are her uncles.
Strýček is a diminutive. Strýc will be more likely found in official documents or statements about some family relationships. It is more common in the speech of some Moravian dialects.
In spoken word the most common is "strejda" but the "ý" -> "ej" is a sign of Common Czech, not Standard Czech.
You can check this comparison http://syd.korpus.cz/QI7SCGxU.syn Some of those words have some specific meanings or are used in some specific situations, like the "strejc" or "strejček", even without meaning a relative.