Mac suddenly deleting items

Hi there. Thanks for reading this. My macbook air, running OS X 10.9.5 (13F34), has started to react to some sort of infection (I think). I noticed it in Chrome after a recent system update: A small video window on the lower right of the browser would appear and try to load. This went away after an hour. Then while using Gimp, the script-fu got hung up. I was able to force quite the script fu but suddenly found that I couldn't export images. Restarted everything to find:

Microsoft word files deleted and I;m unable to open the application. Error message -10810
Gimp, Chrome, Final Cut, Motion, Skype and many others have all been deleted. They don't show up on spotlight but you can see them (with the generic application icon) in the applications folder. Clicking on it only says there is a problem.

When I look in the Terminal, I see this sort of message for each of the applications missing:

9/20/14 9:11:41.008 PM avast![2098]: Deleting '/Library/Audio/Apple Loops/Apple/Final Cut Pro Sound Effects/Motions & Transitions/Title Flange Sweep 02.caf'

What I notice is that Avast is at the start: Has Avast been corrupted in such a way that it's now deleting files? Is this possible? The free version of Avast has been running on this air for a year. Just ran a full scan and found 14 infections:

Win32:Trojan-gen
Win32:FakeMail-M[Tr]
Win32:Kryptik-OAP[Tr]
Win32:VBinject-AI[Tr]
Win32:iBryte-BY[PUP}

There are 228 unscanable files.
Also, I often see on Safari & Chrome the InstalMac page, suggesting that this got downloaded at some point. Not sure if there's any genieo files. Didn't notice any but I'm not really experienced in this stuff.

Any help would be greatly appreciated. Many thanks,

Caseous

Just noticed that not all terminal items have Avast:

9/20/14 9:10:54.319 PM avast![2098]: Deleting '/Applications/Microsoft Office2011/Office/MicrosoftOffice.framework/Versions/14/Resources/en.lproj/strman_00af.strings'

Sorry but I don't think any of my scanners will run on an apple machine. You may have to save all your important data and do a re-install of the OS.
Please try this one scan.

Please download AdwCleaner by Xplode onto your Desktop.

Before starting AdwCleaner, close all open programs and internet browsers, then double-click on the AdwCleaner icon.



If Windows prompts you as to whether or not you wish to run AdwCleaner, please allow it to run.
When the AdwCleaner program will open, click on the Scan button as shown below.



AdwCleaner will now start to search for malicious files that may be installed on your computer.
To remove the files that were detected in the previous step, please click on the Clean button.



AdwCleaner will now prompt you to save any open files or data as the program will need to reboot the computer. Please do so and then click on the OK button. AdwCleaner will now delete all detected adware from your computer. When it is done it will display an alert that explains what PUPs (Potentially Unwanted Programs) and Adware are. Please read through this information and then press the OK button. You will now be presented with an alert that states AdwCleaner needs to reboot your computer.
Please click on the OK button to allow AdwCleaner reboot your computer.A log will be produced. Please copy and paste this log in your next reply.