Maintenance (free) is simply a slimmed down version of OnyX (commercial).
Maintenance doesn't do anything that Onyx doesn't.
The point really is, not
what you run, but
how. Onyx, in particular, has a very complicated interface but is designed to do a lot of things that Maintenance doesn't. Some of those apps do many of the same things. I'm not sure that having more than one app to do the same thing is useful or even advisable; do they do the same thing in the same or safest manner? If not, which one is doing it correctly? Are they all the most current version for your OS? If they haven't been updated for your OS version, should they still be used?
There were several suggestions in this thread that you have not responded to. The computer is quite a complicated contraption and must usually be examined in a very simple, rational, step-by-step manner. While a shotgun can get rid of the fox in the chicken yard, it won't actually solve the problem. I fear that you are reading them, you feel you can't or don't need to try the suggestions. Of course, getting more than one suggestion a day (sometimes even within hours) can seem confusing and frustrating. But, until each suggestion is actually tried, no one will ever know if it worked.
Your problems sound like a combination of too little RAM and too full browser caches. Browsers like to 'feel' like they are fast. A common way of making that happen is to store every page you visit in RAM as opposed to actually downloading the page(s) each time. You can set the limit on how much RAM they can use (browser prefs). You can clear the caches more often (browser menu). You can easily buy more RAM (check the supplied links above) (although installing it in an eMac may be another story). Once a browser fills available real RAM, it will start trying to use virtual RAM, your hard drive.
Paddy mentioned, that can take extremely long, in computer terms, to happen. Changing browsers will only work if the caches have been emptied before it is started up.
It might not be a bad idea to start reading the thread over, from the beginning and writing down the suggestions as they come up. Then, start trying them, one at a time, and writing down the results. This will obviously take time and patience, as the problems usually take a certain amount of time to actually occur.