What does 'outsize character' mean?

Solution 1:

Something that is outsize (or outsized) is exceptionally large. If used to describe someone's personality, it may mean "larger than life" or flamboyant. It can be positive, but it can also be negative.

Solution 2:

It means the same as 'larger than life', which is to say someone that stands out more than the average bear.

Usual characteristics would be as you describe, outspokenness, noticeable character, either in a jubilant happy way or sometimes in a gruff and loud manner. Usually the sort of person that within a group is the one that tends to be making the boldest statements or acting in a way that draws the most attention.