BSOD three different error codes, and random timing.

Your crash dumps are not showing any finite probable cause. In such a situation, it is better to enable Driver Verifier to monitor the drivers.
Driver Verifier - Enable and Disable
Run Driver Verifier for 24 hours or the occurrence of the next crash, whichever is earlier.

   Information

Why Driver Verifier:
It puts a stress on the drivers, ans so it makes the unstable drivers crash. Hopefully the driver that crashes is recorded in the memory dump.

How Can we know that DV is enabled:
It will make the system bit of slow, laggy.

   Warning

Before enabling DV, make it sure that you have earlier System restore points made in your computer. You can check it easily by using CCleaner looking at Tools > System Restore.

If there is no points, make a System Restore Point manually before enabling DV.

   Tip

• If you fail to get on the Desktop because of DV, Boot into Advanced Boot Options > Safe mode. Disable DV there. Now boot normally again, and try following the instruction of enabling DV again.
• If you cannot boot in Safe mode too, do a System Restore to a point you made earlier.

Let us know the results, with the subsequent crash dumps, if any.

Code:

BugCheck 50, {fffffc0004d3f7ab, 0, fffff800032bbbef, 7}


Could not read faulting driver name
Probably caused by : memory_corruption ( nt!MiAgeWorkingSet+425 )

Followup: MachineOwner
---------
MM_INTERNAL_CODE:  7

CUSTOMER_CRASH_COUNT:  1

DEFAULT_BUCKET_ID:  VERIFIER_ENABLED_VISTA_MINIDUMP

BUGCHECK_STR:  0x50

PROCESS_NAME:  ccsvchst.exe

CURRENT_IRQL:  0
===========================================================================
BugCheck 1A, {31, fffffa800c9b3810, fffff88009657000, fffff8a004975203}

Probably caused by : ntkrnlmp.exe ( nt! ?? ::NNGAKEGL::`string'+7271 )

Followup: MachineOwner
===========================================================================
BugCheck 50, {ffffd8a002b9eca0, 1, fffff880016b0c2f, 7}


Could not read faulting driver name
Probably caused by : Ntfs.sys ( Ntfs!TxfAccessCheck+9f )

Followup: MachineOwner
---------

Scan the system for possible virus infection.

• Anti-rootkit utility TDSSKiller
• Windows Defender Offline

As a test, uninstall Norton and all Symentec products using Norton Removal tool. We have seen a nice number of similar issues with Norton installed, both memory and Ntfs corruption. If you want arguments I can supply; but your dumps till now are saying noting against it. Suggesting it based on my experience only.

Use Microsoft Security Essentials as your antivirus with windows inbuilt firewall, and free MBAM as the on demand scanner.
Download, install and update those, and then run full system scans with both of them, one by one.

Test your RAM modules for possible errors.
How to Test and Diagnose RAM Issues with Memtest86+
Run memtest for at least 8 passes, preferably overnight.

Let us know the results.