Ok, I fiddled with it more today and I think I've got it working properly (or, at least, it says that it successfully syncs now rather than hanging on it or crashing). I should note that the following is me trying to remember everything that I did but I might have forgotten something.
What I did (and not sure how much of this was necessary) was
1) Ran the Onedrive troubleshooting program found near the bottom of the following page:
Troubleshoot OneDrive sync problems - Windows Help
1a) Let the troubleshooter do its thing on default settings. I sent info to Microsoft and had it reset Onedrive settings but didn't re-enable UAC settings which are apparently required for Onedrive to work (???)
1b) The first time it seemed to freeze on doing Onedrive maintenance so, after a couple of minutes, I closed it, especially since there was no CPU activity. This had happened all prior times I had run the troubleshooter.
2) Next, I uninstalled the Onedrive entry in the Programs and Features list and ran the troubleshooter again. Sent diagnostic info again to Microsoft and didn't re-enable UAC. This time, it actually got to a summary of changes performed. Cool!
3) Now, I manually re-enabled UAC through Control Panel to its default setting where it dims the desktop.
4) Re-ran the troubleshooter utility, didn't send info to Microsoft, reset Onedrive settings, and it got to the summary screen again.
5) Tried resuming sync which I had paused before step 1. It was still endlessly attempting to sync. I manually shutdown Onedrive by opening the Command Prompt, changing directory to Windows\System32 and running "skydrive /shutdown". After a few seconds, I restarted Onedrive by running "skydrive". This also failed to allow syncing to resume.
6) Thinking that perhaps some settings may have been changed, I restarted, and voila: it appears the Onedrive no longer crashes and, when manually told to sync, it actually starts and reports successful sync!
Although I have noted every step I took, I'm pretty certain that the only steps required are to uninstall Onedrive from Programs and Features, turn on UAC, run the troubleshooting utility, and then restart. Let me know if this works for you (not Sihaz since he had a different problem)!
EDIT: OMG YES IT WORKS! Adding files through the Onedrive app actually update now on the website. Prior to this, it would say that it had uploaded the file but never actually did.