thumb drive issue

Are you plugging the drives directly into the computer, or into a hub or the keyboard? If the latter, try plugging into the computer's USB ports. USB ports on non-powered hubs and keyboards often fail to provide enough power to make thumb drives mount.

Also launch Image Capture and see if the images appear in that app. It is part of OSX so nothing to buy.

How is the thumb drive formatted. If you don't know, in Finder locate it and selection it and then Type Command + I . It will pop up with a window that and one item is how it is formatted. If it has never been formatted, chances are it is NTFS and Mac OS will not write to NTFS. This means it must be formatted to a format Mac OS can write to.

What do you intend to do with the data, if you intend to share it with a PC then that matters!!!

Do they show up in the sidebar in Finder? If not, do they show up in Disk Utility? You can find Disk Utility under Applications > Utilities or by pressing F4 for Launchpad and opening the "Other" group.

If your Firewire or USB isn't recognizing any device.  A solution which has worked for some whose hard drive became invisible in 10.4 was simply to follow these four steps to reset the Firewire/USB bus:

1. Shut the machine down.

2. UNPLUG the power lead to the computer and any firewire/USB drive or devices.

3. leave it for 10 minutes.

4. Connect back up and reboot. 

http://www.macmaps.com/firewirebug2.html

In Finder, Preferences, General: is external drives selected?

Do they show up in Disk Utility?

Are these USB3 or USB2 Sticks?

Is the Mac USB3 or USB2?