Can you upload the contents of c:\windows\minidump to SkyDrive and provide a link?
Consider the following general guidance for dealing bluescreens.
Consider running chkdsk on all partitions. Let chkdsk complete on each partition and see if that helps.
Also consider running SFC /SCANNOW.
If you boot into safe mode, do you still experience bugchecks? What about if you do a clean boot, or device clean boot?
Consider testing memory with Windows Memory Diagnostic or memtest86. Note that memory that passes tests is not necessarily good memory - it just hasn't failed a test. Consider systematically eliminating RAM from the system - run with a couple of modules for a while, and see how things go. Then try the other modules.
Other common suggestions include ensuring drivers are up to date, as well as ensuring that you're using the latest BIOS.
It can be helpful to use Driver Verifier. To enable Driver Verifier... start->verifier.exe->OK->Create standard settings->Next->select driver names from a list->Next->sort by Provider->select all non-Microsoft drivers->Finish, and OK your way out of the dialog.
Then, reboot and use the system as you normally would, and wait for a problem. In the event that the system does not boot completely after enabling driver verifier, boot into Safe Mode and run driver verifier, and tell it to delete the changes.
Wait for a bugcheck to occur after enabling verifier as described, and then upload the dump to your SkyDrive, and provide a link.
Disabling DEP/NX (for IE8) as you described would not seem to have any direct relation to the disappearance of the problem, but it may be that it is changing the code path enough such that the bug is not triggered at some later time.
Bugchecks / BSODs are caused by faulty hardware or buggy/incompatible drivers, not user-mode programs like Internet Explorer or a web browser.
Do note that by disabling DEP for IE, you've turned off a defense-in-depth measure; a better option would be to use components/add-ons/plugins that don't violate the DEP protections. Perhaps a Java update would take care of the problem with the java app you encountered the problem with.
I suppose, that re-enabling DEP for IE will cause the bluescreens to return? Have you tried this?
Looking at a previous 0x44 bugcheck - !irp on the IRP address indicates that the thing at that location is probably not an IRP. This would perhaps suggest some kind of corruption. Looking at the part of pool associated with that address, it seems to be associated with tag NDCM. Tag NDCM is associated with some Symantec product; you appear to have such a product installed.
So, to test the issue, you could uninstall the Symantec software on your system, to see if it may be contributing to the behavior. (Don't just disable the software - uninstall it, to remove the drivers from the Symantec product.)
But ultimately, the 0xa bugcheck pretty clearly flags the oz776.sys driver as the culprit; seeing that driver also flagged in the 0x44 bugcheck would seem to add further evidence against it. However, if you wish to try something other than not using the SmartCard reader or letting the party responsible for the driver know about the problem, you could try the aforementioned suggestion regarding the Symantec software.
I ran the CD version of Blackberry software with no issues for three or four months early 2010. After one of the updates I started getting the blue screen error. My system crashes 4 to 5 times per day. Usually after a period of inactivity, not always. Due to a Virus I elected to do a clean reinstall of windows XP pro. This stopped the blue screen. I installed all of my software (excluding Blackberry) and ran error free for two weeks. I finally had to install so I could update my Phone for a trip. Again I started with CD and ran fine for 4 hours. Software indicated it needed to up grade, I had hoped I could skip the defective upgrade. No such luck, 30 minutes after upgrade the same blue screen I had before. I uninstalled Blackberry , same blue screen error. I tried to do a system restore, systems restore will not restore to earlier time either.