Grad students/postdocs taking ideas with them, what's normal? If a graduate student or postdoc develops or plays a large role in developing an idea (this could be anything from a new experimental method or new code for running simulations), what's supposed to happen when they move to a new institution? 

Can they use these ideas on their own after the move, share them with their new PI/colleagues, use them to get their own funding? I assume the answer is generally yes, but


what if the idea is unpublished with the original group? 
does it depend on the idea, code/scripts vs. less tangible ideas?


Just not sure what's the normal protocol or if I'm assuming incorrectly.
I think the main thing you should keep in mind is, did it seem like people in your old lab/group will be or would like to be working this?  You don't want to end up "stealing" someone's project, or competing with them.

There's a difference between an idea you've come up with completely on your own, and something you've come up with together with other people.  For ideas of the latter type, it's reasonable to suspect that your former colleagues may still be thinking about this.  In addition, if they contributed significantly to the ideas, they should have a chance to be included in the project.  If how the other parties feel about working on this idea is not clear from your prior interactions, just talk to them about it.