As for actually overpowered, Alicia from Valkyria Chronicles is ridiculous.
It's kind of crazy, but Avan from Valkyria Chronicles 2 might be even more overpowered than Alicia was. Being the only character in the game who can change into any class from any of the five main class trees, Avan is also the only character who can get Battle Skills (class-specific Potentials) from any class. And some of the Battle Skills Avan can get are completely nuts; such as "Double Action", which lets him occasionally perform two actions in one activation. He can also execute boosted power support attacks with any other squad member.
Of course, the CP cost 1 Light Tank from Valkyria 2 was also pretty overpowered. A tank having the same activation cost as a regular soldier is just really good. It's not the biggest tank nor the most heavily armed tank, but it is still a tank!