Hank, my experience over the years has taught me that most apps which claim to accelerate your Mac are shams. Your machine cannot run any faster than the processors which are in it, no matter what anyone tells you to the contrary.
Going by what you have stated above, your main problem seems to be that your hard drive is jam packed with data; in fact, way too much data. Everything that I have read over the years suggests that in order to maintain optimal speed and performance, your hard drive should be no more than 50% full.
Once you past that suggested mark, what happens is that your machine begins to slow down more and more, as you continue to fill up your hard drive space. This means that the head on your hard drive has to take more time to seek and find empty blocks in order to write new data to the hard drive, and more time to find the bits and pieces of programs which have become fragmented all over your hard drive, due to your constantly writing new things to it, and deleting old and unused things from it.
I have used a variety of the products which are mentioned above, including TechTool Pro, Onyx, Disk Warrior and a few others. They all certainly help in different ways, and you will definitely notice an improvement in performance after using each one of them.
However, my key point is this: There is no magic bullet app which will fully resolve the issues which you are currently experiencing. In fact, if any of them are used the wrong way, you can totally fry your hard drive, or at the very least, lose a lot of files which you cherish, because many of them have the same name, such as your multitudes of image files.
The bottom line is this: To really resolve your issue, you need to apply some elbow grease, and invest your time in manually deleting the programs and files which you no longer use. Some of the biggest offenders will be audio and video files. Collectively, they can gobble up hard drive space in no time at all.
One app which I use on a regular basis is CleanApp. Whenever you add a new app to your hard drive, CleanApp will take note of it, along with any other files which are associated with that program. Then, if at some later date, you decide to trash that app, CleanApp will activate and show you all of the files which are associated with that app, and give you the option to delete them. It will also suggest other files which may possibly be candidates for deletion as well.
However, as with other apps which perform similar functions, you need to be very careful that you don't delete files which your system needs, or which are used by other programs as well.
All in all, programs such as Onyx, Cocktail, Deeper, etc., will run certain built-in maintenance scripts and perform other cleaning functions. CleanApp does this as well. However, given the overall size of most modern hard drives, running them will regain you very little hard drive space by comparison.
Similarly, running programs such as TechTool Pro, Disk Warrior, Drive Genius and Disk First Aid will repair file directories and block issues if they are not too severe. Some will also optimize your hard drive by eliminating file fragmentation, although the advantage of doing the latter has been a source of debate with some people.
But again, what it really comes down to, even after using all of the above programs, is that as long as your hard drive is overly full of data, your machine will remain sluggish, because it is like a drowning man trying to grab a last gulp of air. You need to free up more hard drive space by manually deleting a lot of the junk on your hard drive.