Software/App for electronic research notebooks
For the last month, I have been using Gitit for this purpose.  That link goes to a live demo where you can try it out.  It satisfies all your requirements:


It's a wiki, so you can easily make links between pages.
It's built on pandoc, which understands TeX and uses MathJax to render it (it technically renders a subset of TeX, but it's a pretty substantial subset)
It's actually a Git repository, so you can upload anything you want to it.  Or just put your figures out on the web (via figshare or a public Dropbox link) and link to them.
Same as 3.
Again, it's Git.
It is open source: https://github.com/jgm/gitit


As a bonus, you can put it out publicly on the web if you want (or just run it locally on your machine).  I run it on an internal server at my University and my students and post-docs use it to.  Thus it's a convenient way to share information as well.