More nebee than nebee
 

I am an internet junkie I believe you should beable to not only protect yourself but others while on line. Security is big issue. Like running most Programs on usb or memory cards for security reasons.can linux be run on a memory card or usb type hard drive?

Yes. For instance if you want to use it on an USB hard drive you can have a look here. And you could use a memory card as well.

I don't understand how this could "not only protect yourself but others while on line", though.

Of course!
Try reading about DSL (Damn Small Linux), Puppy, or I suggest bodhi
http://www.bodhilinux.com/

even large distros like ubuntu run on stick using "Sturtup Disk creator"

I advise against Damn Small Linux. It seems to have stopped being maintained. Never used Puppy Linux in-depth and never used Bodhi but they seem pretty lightweight.

DSL has the goal to be able to run on i486. So it is not state of the art.
I haven't use puppy in looong time.
I tried bodhi for a wile yesterday and it seems good.
Of course if you don't mind computing power you can run ubuntu from the stick.

Those things are not mutually exclusive. Slackware also can run on a 486, but it is state of the art. DSL is not maintained since 2008, this means that any security hole found til then is not fixed and will never be fixed in DSL. So recommending it to a user who is concerned about security does not make much sense.

@Gray Matter: Basically any distribution is able to run from USB or a memory card. If you are concerned about security may be LPS is the one for you.