iMac G3 booting by itself Please Help!!

How long had it been since its last successful boot? If it has been off wall power for longer than the few minutes you disconnected it this time, the internal backup battery (the "PRAM" battery to most of us) is likely dead and that can cause startup issues.

Is this a tray-loading or slot-loading iMac G3? Do you remember what OS is on it?

Some version of the macOS have a preference setting that will turn the computer on following a power failure. I don't have access to a working pre-OSX system at the moment so can't check where it is, but I'd hazzard a guess it is under an energy saving pref.

Do you have the system install/restore disks that came with the computer? If so, try starting from that disk instead by holding the c key at boot.

Once we know the sub-model we can better advise if there are known issues.

Does the power actuator button seem to push in and release normally? When you re-energized the power strip, it's possible that the iMac's power micro-switch or other component took a surge, creating a permanently closed circuit. Those micro-switches can fail after repeated use, but if you typically use the keyboard to power on the computer, that could suggest otherwise. Perhaps it was going to happen the next time it was powered on, and had nothing to do with the interruption of power from the strip. Is the power strip only that - a multi-outlet distribution strip, or does it include surge protection? If the latter, does it have LED light(s) to indicate that the protection is still functioning?