"Have heard you can get better reception on these radio if you attach an alligator clip to the end of the telescopic antenna attached to a larger outside or indoor antenna. The few times I've tried to use it I can't pull in anything but regular radio stations, a few garbled sounds on the other bands but nothing readable."
The trouble with that notion is the majority of portables are overloaded by strong signals hence the garble. You can hear "regular" AM stations because that section only uses the internal ferrite rod antenna but the shortwave section relies on the telescopic whip and is designed for optimum reception using it alone. It's hard to explain without all the techie stuff but basically it's too sensitive to handle more input than the whip provides.
Again without getting too technical about the best you can do with that sort of receiver is lengthen the antenna just a bit by connecting 10 or maybe 20' of wire to it but no more. Just toss it across the floor and roll it up when not in use, if you still have garble roll it up a little at a time until things clear up and leave it that way, the excess wrapped with a bit of tape.
I would avoid any connection to the wall outlet, that mounting screw is grounded and would make the radio itself part of a giant loop antenna, the AC side of it being also part of the loop. Look at it this way, at the service entrance panel there is a grounded bus bar with the afore mentioned screw and the U shaped blade slot connected to it through a safety ground wire within the power cable. Also in that cable connected to the ground bus is the AC neutral connected to the wider of two slots in the outlet. The narrower slot is the hot lead that eventually goes outside to the pole and may be disregarded for the sake of this discussion. Now visualize the loop back to the bus, the AC neutral being one side and the grounded screw being the other and the radio right in the middle. This makes for more antenna than the radio can handle from an overload point of view AND being part of the AC mains wiring will pull every little bit of static and noise generated by everything on the block, switches opening and closing, fluorescent lamps, dimmer switches, home appliances and everything under the sun channeled right into your radio.
Funny how you remind me of myself and my Frankenstein lash ups when I first started out in the hobby. I had old radio chassis scrounged from the junk pile behind the local repair shop, car radios from the junk yard, transformers, batteries and loads of wire all over the place and somewhere in the middle of it all was a mother shaking a broom and screaming "You better get this mess cleaned up before your father gets home!" My radio adventures taught me one thing about moms and late night DXing, if they don't have radar or some extreme sensitivity to electromagnetic waves at least they have ultrasonic sonar hearing that can pick up the tiny vibrations of a set of headphones at barely audible volume from a thousand yards and homing torpedoes that'll get you every time. Uh oh, I hear her coming up the stairs... Down periscope, DIVE DIVE!!!