Uninstall avast but still have blocked websites

From your description, it seems that the malware still exists. It probably is a recent nasty version of VSearch. Check the instructions by Linc Davis in this topic: Macbook Adware/Spyware/Virus

Assuming you can load the page, follow all the instructions in this Apple Support document: If Safari doesn't load a page or webpage items are missing - Apple Support.

If you cannot load that webpage, please boot Safe Mode by following these instructions: OS X El Capitan: Start up in safe mode. While in that mode, load the page referenced above, follow its instructions, and then reboot normally.

If you still cannot load the page or if following the above instructions doesn't fix the problem, reinstall OS X: How to reinstall OS X on your Mac - Apple Support.

To properly uninstall "Avast" you should use its uninstaller, which will completely remove all its components. Using "cleaning" apps is not recommended, under any circumstances.

The most recent version of "Avast" installs what can only be described as adware, and as such, is indistinguishable from malware itself. Don't use such things, since they can only increase your system's exposure to malicious interference. Excerpted from Effective defenses against malware and other threats:

Never install any product that claims to "clean up", "speed up", "optimize", "boost" or "accelerate" your Mac; to "wash" it, "tune" it, or to make it "shiny". Those claims are absurd.

• Such products are very aggressively marketed. They are all scams.
• They generally operate on the flawed premise that a Mac accumulates "junk" that needs to be routinely "cleaned out" for optimum performance.
• Trial versions of those programs are successful because they provide the instant gratification of greater free disk space.
• That increased space is the result of irreversible destruction of files, programs, or operating system components normally protected from inadvertent alteration or deletion. The eventual result will be unreliable operation, poor performance and random crashes that may not become evident for months or even years after their use, when updates to programs or OS X are eventually released.
• Memory "cleaners" that circumvent OS X's memory management algorithms work by purging inactive memory contents to mass storage, which can only result in degraded performance and accelerated hardware failure.

The only reliable defense against adware is its recognition and avoidance. To learn how to recognize adware so that you don't install it, please read How to install adware.

Try running this program and then copy and paste the output in a reply. The program was created by Etresoft, a frequent contributor. Please use copy and paste as screen shots can be hard to read. This will show what is running on your computer. No personal information is shown.

Etrecheck – System Information

Please download and install EtreCheck from http://etrecheck.com/

Run it and post the report here.