Java and Flash Player do not work on Chromium
Unfortunately Google seems to think they know better than everyone else what people need to use online...

Here's the deal. They've deprecated those APIs, meaning if you want Java/Flash to work, you're out of luck.

HOWEVER, they haven't been removed yet, merely disabled. It'll get removed in a couple of major versions, but you can still force-enable them in the short term. This WILL stop working when Chrome 45 comes out in a few months. The only alternative then if you need Java/Flash will be to switch to a different browser.

In short:

For PPAPI plugins, go to chrome://plugins, scroll to the plugin, hit Details, and Under "Type: PPAPI," click Enable.

For NPAPI plugins, go to chrome://flags/#enable-npapi. There's an option there that says Enable NPAPI. Toggle that, and restart the browser.

I'd suggest getting used to Firefox or Safari in the meantime :(