Three of your minidumps pointed at Avast's driver (i.e. aswMon2.SYS, TS: 15-Sep-09). Two were 0x1A errors, with one of them 'Memory_Management' error.
Can you please provide me with your system's complete specifications including PSU specs/make/model?
Please download and run memtest (you can get it from TechSpot's downlaod section), and run it for 8 passes, to check whether RAM is the real cause of this.
Also check whether there are program updates available for Avast you are using almost an year old release of that software I think.
Lastly, do ensure that your system is clean/dust free.