XMPP

Clients

• Gajim
• Android app (open source but not free)
• iphone client (untested)

Servers

There are several server implementations that you can run on your own. Best seems to be:

• OpenFire
• ejabberd - I tried and failed to get this running - it has hundreds of open tickets

Free server with secure group chat via OMEMO

You want to find a free XMPP server that is current enough to support OMEMO.

• Register on the website of this xmpp.social server.
• Add an account for it to Gajim, and connect.
• Create a new room! Set a password. Check members-only. You should be able to then turn on OMEMO!

Incabable XMPP servers

On these (older?) servers, Gajim always says "group must be non-anonymous and member-only" even though I'd set it that way.

• https://www.kode.im/
• jabber.calyxinstitute.org