Upvote:3
ESTA is needed.
In order to prevent F1 visa usage for reasons unrelated to the study, F1 visa must be accompanied by a proper visa document (I-20) and valid, current SEVIS record (created by your school designated official, maintained by the CBP/ICE). Since you have graduated, your I-20 is invalid, and your electronic record in SEVIS has been terminated.
Upvote:8
Yes, you need the ESTA.
Traveling for a funeral is not a valid purpose for an F1 student visa.