This is weird:
For this site: oiltradingbroker.com
On google, the homepage’s meta title tag appears as: “oil trading broker”
the sites true meta title is:

“Crude Oil Trading Systems, Tips, and Guides To Forex Trade”</pre>
On yahoo the true meta tag appears.
Anyone knows why this happens?

The site's "home" page probably has a listing in DMOZ so Google is using the rather lame title and description from there.

AND it is a TITLE element NOT a "meta title"

the site is not listed in dmoz.

There can be multiple reasons for such.
1. Your blog title is Oil Trading Broker but your home page title is different from your blog title and it could be that Google visited your site when you had the blog title as your home page title.
2. You have <link rel='index' title='Oil Trading Broker' href='http://www.oiltradingbroker.com/' /> and not sure why you have it.
3. You may have submitted your site to some other directory like Yahoo Directory with that title.

Cache site time is not visible because of those header images but what I can sense is when Google cached your site you had that as title.

That's Google "Dynamic title" feature where the display sistem will change what is shown as the SERP title to ome text from the page that matches the users search query better than the title element does.

In this case the title is coming from the first heading on the page.

They have been doing it for a fair while now