What deeds that are 'not normally done' did Avimelech and his subjects suffer?
Rashi: He blocked all the human orifices - those of the Zera, of Ketanim and Gedolim, the ears and the nose.
What was Avimelech accusing Avraham of?
Seforno: He was accusing him of causing so much damage to a person whom he did not know and with whom he had not fallen out. Moreover, he gained nothing from the harm he was causing him.