As you are getting the error on the line
ddldegree.DataSource = dt_degreess;
And it is the first reference to ddldegree after the declaration:
DropDownList ddldegree = gvOtherDegree.FindControl("ddl_degree") as DropDownList;
Then either "ddl_degree" does not exist as a findable control, or it is not created as a DropDownList. Either one would give you a null value and cause the error.
Check your control name, and then check it has "runat=server" in it's definition.