Ps3 – install PS3 games on an external hard drive

From How to upgrade your PS3 internal hard drive:

Things you will need

1. Larger SATA notebook (2.5″) hard drive (hd), 5400rpm or 7400rpm.

So unfortunately with your 3.5" hard drives you are out of luck - they won't fit into the PS3 and they are the wrong type (ATA vs. SATA).

However, all is not lost. From the same site there's a post on How to add an External USB hard drive to the PS3

If you have amassed plenty of videos, music and pictures on your computer over the years then why not stick it all on an external hard drive and hook it up to your PS3. Easier, and much quicker, than streaming files over your home network this is an ideal solution for users with massive hard drive needs.

With the advances in the PS3 software, many video types can now be played and nearly all music and picture formats are also available.

So if get hold of a 3.5" enclosure with a USB interface you should be able to use the drives like this.

IF you mean an external drive or somehow hooking your PS3 to your PC no, you can't install games on an external drive like that. You can however use a laptop 2.5" HDD and replace the physical HDD inside the PS3 (you can backup and restore your current saves to keep all your stuff too).

See this question for a bit more info on the HDD type you need Internal PS3 HDD Replacement