What was the strength of the Empire's fleet around the time of the Battle of Yavin, specifically capital ships (star destroyers, dreadnoughts, etc)?
According to C-canon EU (Timothy Zahn's "Specter of the Past"):
But it was. And down deep, Pellaeon was sure Ardiff knew it as well as he did. A thousand systems left, out of an Empire that had once spanned a million. Two hundred Star Destroyers remaining from a Fleet that had once included over twenty-five thousand of them.
Whether that number was close to the maximum stated at 0ABY is unknown, but presumably it was correct order of magnitude.
 - obviously, post-ROTJ C-canon has been "Legendized" by Darth Mickey as of 2014, so YMMV in how you personally assess the canonicity of this factoid