outside outlet damage problem

I have an outlet in the entryway to my house on the outside. A few months
back I plugged a circular saw into it and the outlet melted with a black
plume of smoke and fused part of the extension cord plug in the socket as I
began cutting.

I replaced the outlet and it seemed to work ok after that. I also replaced
the fried plug on the extension cord. It's a heavy gauge cord but don't
know the exact gauge.

Did the circular saw work with the extension cord after that?

The other day I tried to use the same outlet, same cord with an electric
hedge trimmer and the plug began smoking where it connects to the trimmer.
Also now the trimmer is on all the time, whether you depress the trigger or
not.

What you are describing bothers me. It is possible that the
outlet was wired wrong (reverse polarity) so I would check
that first. You did not mention if a breaker or a fuse popped.
If one did not pop, I would very serious concerns about the
wiring in the house.

I haven't tried this cord in another outlet yet, kind of wary of frying
another electric tool. Does this sound like an outlet problem, or an
extension cord problem. I got the screws good and tight on the replaced
cord plug, also got them tight on the new outlet in the house, did not use
the "backstab" holes.

Interesting problem. Reverse polarity wouldn't make any difference. The
worst the extension cord can do is cause excessive voltage drop; if it were
shorted, it should trip your circuit breaker. I suppose it is possible that
you have both a shorted extension cord and a defective breaker.

Other than that, you should check the voltage on the outlet. If it is
normal, I would replace the circuit breaker for lack of a better idea.

I hope it's an extension cord problem. How old is the cord?

Although I'd bet it's not the problem, pick up a circuit tester and double
check that the outlet's wired correctly, even if you're sure you replaced it
correctly. You never know what nonsense could be lurking further down the
wire. I suspect the extension cord's the real issue. Since nothing's
impossible, there could be a problem somewhere other than at one of the
ends, and you may be able to diagnose this using a multimeter (or just your
eyes). Hack a little from both ends and use the meter to check for shorts
between the various conductors. If you have any doubts at all, chop the cord
into uselessly small pieces so nobody else tries to salvage it, and get
yourself a new one.