Hi, Suzanna! Glad to see a new/old face--lol!
Many groups which say that there needs to be an invitation in order to join were actually effectively closed by the last person who ran the site (EddieDingo) because the group's creator had left TBD and the group was no longer active.
Most of the groups which are still active are open membership and need no invitation. It's kind of difficult to know which groups they are because the active groups don't all show up on the first page of the "Groups" tab. You just have to look through the pages of the Groups section and watch for groups which have been active this year (and possibly last year) then go there and join.
Some groups which I know are open and/or active are:
And there are others, I'm sure. If you encounter a group which appears to be active and requires an invitation, the thing to do is contact the group's creator. I'm pretty sure they'll let you in.
Hope this helps.
One way to find active groups is click groups tab and sort by latest activity. Best sort.
HAHA! Yeah, "Latest Activity" is the easiest way. Last time I tried, it didn't work; but now it does. Hooray! ("Most Active" obviously still doesn't work.)