Group pages in multiple ways

I’m trying to migrate http://oicjapan.org from Joomla to WordPress, and the current nut I’m trying to crack is how to handle the short blurbs about regularly occurring events (see the “Schedule” and “Events” menu items on the old site). Because the information is somewhat timeless, my first thought would be to use pages rather than posts, because posts normally show dates. But without categories and tags, I don’t know how to achieve the effect of grouping the items two ways (type and day-of-week) and showing all events in a selected group. Parent page is one way, but it has oddities, and it’s only one.

I looked for an event plugin, but everything I could find treated each occurrence as a distinct thing, so they required start and end dates for reoccurring events, which is kinda silly for something like the worship service for a church that is 40 years old and doesn’t expect to close anytime soon. In Joomla the events were simple articles (like pages in WP), so I don’t need fancy event handling or calendars or anything.

What would you guys suggest? Is there a plugin that would help me group pages in at least two ways (using metadata or something) and then display them one after another? Or is there a way to use posts but make them look more timeless in these particular views (I don’t want to hide the date for the whole site, because in the case of church news items or something, we might want to use posts the normal way).

Extra credit if you also know a plugin or something that could list all the events in one place, grouped by type – preferably in a way where people can peruse more info without leaving the page. See the first menu item under “Events” and notice how you can expand items of interest.