[IANAL]
In the absence of a vesting schedule, I see little legal reason that the options did not vest immediately. The primary reason for a vesting schedule is to prevent immediate vesting of options from occurring.
Lack of a vesting schedule is, in my experience, pretty common among less sophisticated [for some definitions of "sophisticated"] founders. It sounds like this a case where it worked out as well without one since you stayed past a typical vesting period.
That said, exercising and liquidating the options is likely something that should be reviewed by an attorney irrespective of vesting schedules or an immanent intent to leave the company.
Good luck.