The difference in the wireless connections speed value is normally based on the capabilities of both the WAP and your adapter card in your computer. It does not necessarily show the strength of your signal, more the connections ability to accurately transmit data at designated speed values ie. 1Mb/s, 54Mb/s. I do not know enough of the Linux world to help with the troubleshooting that I would recommend. But If you can get some help from someone more Linux savvy the go for it.
First thing that I would do is test your computer on a different WAP. If the connection is stable then you would need to go into troubleshooting your WAP which I will cover a little further down the post.
If in the event the connection is still shoddy and bouncing around then I would recommend un-installing your adapters drivers and ensuring that you have the most updated version for your card/OS. Once you have done that then I would use the software available for your adapter and set the link speed to match the link speed of your WAP (Most WAP's will state capable link speed somewhere on a sticky tag or sometimes right on the top of the case).
If you are still having trouble maintaining a stable connection then I would try a USB wireless adapter to see if maybe your on-board is having some issues. I do not recommend using the standard Wall-Mart available adapters, but they do the job in most cases. Install all the software and make sure it is up to date and test you connection again.
Okay, with WAP's first off I would log into the WAP and ensure that all your tx/rx settings set set to their highest levels. Also most WAP's will have a firmware update option built into their configurations page. If not then you can always go to the manufactures web site and see if they have newer firmware and instructions on how to update your WAP.
If you have any questions or need me to walk you through any of the hardware settings just let me know by email. email@example.com
Hope this helps you out!