I see a number of posts on various plugins for doing an Event Calendar that work with Wordpress, but the free hosted version does not allow me to use these. Are there any solutions that would work for hosting a calendar of events for an organization that I volunteer for? Even embedding a Live/Google calendar would work, although I understand that iframes are also not allowed. Thanks!
It may be time to give up WordPress.com. There is little day to day difference in managing a self-hosted version, but there is a world of opportunities that will open with a few well selected plugins. You mentioned you're volunteering for an organization. If the issue is paying for hosting, Dreamhost and HostGator offer free lifetime hosting for US based 501(c)3 non-profits. Dreamhost's process is the easier of the two. (Disclosure, I'm an affilate for both...but look ma, no links).
Between free hosting and plugins, your organization's events should get all the attention they need.
Simply: If they don't allow installing plugins, then you'll have to accept that. No one over here can do magic tricks. (Btw: without link to hosting details, etc. it's only guessing.)
Why don't you simply get a really cheap hoster like 1-3$ / month? I ain't got one in my mind now, but there are some.