Not shifting into smallest rear sprocket/squeeking noise

[buzz]

I have a problem that I have tried to fix, but cannot seem to get anywhere. A couple of days ago, I cleaned the small sprockets on the derailer and suddenly there was a loud sqeak that only occured when I was in the second smallest cog. I also noticed the chain was really straining to get to the small top cog on the derailer and if I pedaled backwards, the chain would eventually stop going and lose tention. It is a 21 speed bike. I also noticed that I could not go to the smallest sprocket. It also jumps off the top sprocket into the spokes. I live in a pretty flat area so can get by without jumping to the highest cog, but still would like to get it fixed.
My bike is very heavy on the drive side and loves to tip if a small breeze comes up and the rear derailer has been smashed several times and I am wondering if that may be the problem. When it falls, I play with it a bit and seems to work for a while, but a lot of this happened again when it fell. Or, should I just keep playing with the adjustment screws? I have watched the videos, but did not really seem to notice the derailer moving much, if any, when I was adjusting the screws.
Any help would be great. Thanks.

[cyclerUK]

When the bike has fallen over has the derailleur "mounting" got bent?<br />
Stand the bike up vertical and look at the derailleur from behind.<br />
The jockey wheels should be parallel with the cassette gears and the same when looking down from above. If the mounting has bent than usually it can be straightened with care.<br />
Your description of the chain going loose when pedalling backwards could be a stiff chain link or a jockey wheel seizing or again the derailleur out of line.<br />
If the chain / derailleur catches or jumps then you need to adjust the "stop" screws as well as the general sprocket alignment.<br />
To start with support the bike so that you can watch the gears / derailleur whilst turning the pedals and operating the gears. Some where you should be able to spot the cause.

[buzz]

Thanks for the help. I am still working on it and have noticed two thing. It is a seven speed shifter, but it seems to easily throw the chain into my spokes. It does not want to go down to the highest gear.
Also, I noticed that the mount for the derailer may be bent. This could have happened when the bike feel and it pushed it into the direction of the spokes. Not sure if that is the problem or how to fix that if at all.

[cyclerUK]

If the derailleur hanger is bent then, and if it is steel, (part of frame) it can be straightened. Remove the derailleur and, using a large adjustable spanner, bend / straighten the hanger as needed. (Adjust the jaws of the spanner to make a good fit on the hanger)
This has to be done with care obviously or you could snap it and virtually right the frame off, or take it to a good bike shop and let them do it. You then will have to replace the derailleur to see if it is aligned correctly
I have straightened a hanger with the derailleur still attached but it was an old frame.
If it is an aluminium frame then it may have a removable hanger and this can be replaced with a new one.

[buzz]

Well, chalk this up to one of those things like slapping the side of the TV to make it work or kicking a pop machine to get it to dispence your can of soda. I fiddled and fiddled with it and got the squeak to go away and got it to stop shifting over the cassette into the spokes. I still could not get it to go into the highest gear. But, I had to take off my rear wheel to replace a spoke and when I replaced the wheel, everything works fine.