...but can you replace the Intel core?
Even were a CPU upgrade possible (I don't see that it is) it would accomplish little.
In the days when processors swaps were easier, I found you needed a 40% increase in processor speed to "feel" a real performance difference at the user's chair. Applying that to your 2.66ghz processor says it needs a 3.7ghz processor to be effective in actual use. Unfortunately...
...the fastest Core 2 Duo processor Apple even installed in an iMac was only 3.33ghz.
IMHO, not worth it even if theoretically possible.
The common USB/SSD external boot-volume solution is not available to pre-2012 iMacs. It requires USB3; applying it to a USB2 iMac could mean data transfer rates far worse than you now have.
As for the SSD, your Early 2009 iMac has a slow SATA 3Gb drive bus, handicapping its max speed regardless of drive type. Yes, there are compatible SSDs for the early 2009 iMac:
https://eshop.macsales.com/shop/ssd/owc/imac/early-2009
but, to replace exaggeration with data, an SATA 3GB SSD can do transfers no faster than about 250MB/sec. That would be an improvement over the 60 to 100MB/sec you likely now get, not 20X but more like 3-4X depending on the specs of your current mech hard drive. It would would help some but you still have a bigger problem.
Your macOS version limitation is the real pachyderm in the parlor here. Many web sites now require much higher macOS versions to fully work, and current browser versions cannot be installed on 10.9. You can throw hundreds of $$$ of hardware at the computer and still not be able to use it for browsing the internet. No hardware upgrades can change that.