Writing quite a lot of C# at work, the language feels very much like
what I'm used to
Dart is something to solve that. It's there to give you the stuctural convenience of Java and moreover it doesn't have all these awkward JS features. (Most of them related to weak typing.)
So the answer is yes: classes, inheritance, ...: "traditional OOP". (Most realworld JS webapps out there use jQuery's callback based approached as main structure.) And it has a loose form of static typing, that's however not the key selling point.