The Pirkei D'Rabbi EliezerPirkei D'Rabbi Eliezer does indeed state that Esav killed Nimrod (ed. Higger ch. 31). This is also found in Yalkut Shimoni Yalkut Shimoni (Parashat Tol'dot 110) and Targum PseudoPseudo-Jonathan (Parashat Tol'dot 25:27). It is further quoted by Rabbenu Hayyim Paltiel (Parashat Tol'dot 25:32) and Rabbenu Bahya (B'reshit 3:21)
You are also correct that there is a Midrash that Avraham killed Nimrod. This can be found in TanhumaTanhuma (ed. Buber) Parashat Vayera (2), which identifies Nimrod with Amrafel, and states that Avraham killed him. This is also found in Yalkut Shimoni Yeshaya (511).