Is there any way to turn off the avast pop ups that appear when I start Outlook and Internet explorer?
Hello and welcome 
You mean the splash screen, right ? :
Yes, you can turn these splash screens off. To turn off the screen when you start IE go to Resident Protection Window, choose the provider Script Blocker → Settings → Advanced and there turn off the option Show splash window on startup.
To turn off the splash screen when starting Outlook, go to the Resident Protection Window again and there choose the provider Outlook/Exchange → Settings ->Advanced and there turn off the option Show splash screen when the provider is loading 
This is all you have to do, hope you understood my words ;D
I assume you are talking about the splash screen for the MS Outlook plug-in ?
Hint, the avast help file is very useful ;D
[b]Show splash screen when the provider is loading[/b]. If checked, the provider will show a splash screen when the supported e-mail client is started (MS Exchange client and MS Outlook 95/97/98/2000). It might be useful as an announcement that the e-mail will be protected.