Is there any way to download images from an Olympus stylus tough 6000 to a flash drive or external hard drive without using a computer?

Perhaps I can help????
I don't know how many pictures you already took, but perhaps you did more than 10000? Your camera can shoot pictures in one directory, with numbers 0001 till 9999. When it reached 9999, it will automatically make a new directory and start over with number 0001. Not sure if that happened, but you could look for another directory on your memory card.

Then I do have a question. Do you mind what happens with your pictures when your camera dies? Because I think that is the only place you have all your pictures. (I hope I'm wrong) Or worse what if you lose your camera? Or did you already make backups from your pictures?
Try to make it an habit to backup all your pictures shortly after you took them. And one backup is none backup. At least two backups on 2 different media. Like one backup on your computer, one on an external hard disk, memory stick or DVD.

The problem is in the camera lens, the image sensor or shutter is the issue, it will need the attention of a camera technician.

You can get your drivers and manuals from here:-

http://www.olympusamerica.com/cpg_section/cpg_support_product.asp?id=1446

Having gone two months without a response to my query, I assume my suggestion to use a card reader solved the problem.

In order to use a card reader, you must have a card to insert into it. If you've been using the camera without a card, you've been saving the pictures to the camera's internal memory. In order to get at those, you need to copy them to a memory card first. Your owner's manual will explain the procedure.

You can use a card reader to try to download them to your computer. You could also take the card to a store like Walmart and use one of their picture making machines.

how to transfer videos from my Olympus stylus 760 to a macbook?

Use the "Backup" command. See page 40 of the manual: Owners Manual User Guide for Olympus Mju Tough 6000 Digital Camera

This happened with my camera. Try replacing the card, the card itself may be corrupted. It worked for me when I replaced it.

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You can download the manual yourself  from the manufacturer's web site at http://www.olympusamerica.com/cpg_section/cpg_support_product.asp?id=1224