My dad was a Sr., but he has passed on now, so technically I don't have to use Jr anymore, right?

My dad was a Sr., but he has passed on now, so technically I don't have to use Jr anymore, right?

Wrong. The passing of Sr. does not change the name of Jr. Your name is legally Jr,. and if this is listed on your ID. You must use Jr., not Sr.
The same goes for if II passed and III is still present. III does not get to use II just because they are no longer alive.