At the time of submitting this Idea, it seems that activities cannot be routed in Omnichannel. This is an unfortunate oversight, as it is as important to be able to route activities, as it is to route Cases.

At present, it is possible to add most entities to Omnichannel for routing by enabling the entity for 'queues' from the entity "Communication and Collaboration" section of the entity customization.

Even though Activities (such as Emails, Phone, Appointment, Letters, custom activities, etc.) can be enabled for 'queues', they will not show up as entities that can be routed in Omnichannel. (Incidentally, activities can at present be routed into queues without the use of Omnichannel which is therefore surprising that this functionality isn't now available with omnichannel)

In real world scenarios, Contact Center agents need to deal with many incoming activities (such as emails, chat, social media posts and phone calls) first, before they deal with the actual record (such as Case or Lead). The record (lead or case) is often created from the activity. But before that happens, activities need to be routed to the correct agents first. Omnichannel has advanced routing features but it is a bit pointless if you cannot route the source records (activities) first, which often is the most demanding and highest volumes and then funnels down into records like cases and leads.

If live chat (where chat is a channel) can be routed, surely other activities should be routed too.