You notice they are in 1, 2, 3, 4, with item 1 there is a selection OR so if you only have one of those there will be no potential conflict between the other item 1 suggestions or avast. The main consideration is not having more than one resident anti-spyware as already mentioned.
The item 2 & 3 shouldn't be any problem as the freeware options are on-demand (not running all the time, with TeaTimer off as mentioned), so there should be no conflict with any item 1 selection or avast.
Item 4 SpywareBlaster is a passive prevention tool, neither resident, or on-demand, so won't conflict with the other items or avast.
All you will have is some used space on your hard disk, until you run an on-demand option, only then do they use system resources.