Refers to the journey itself, often with a sense of the route or the experience of traveling.
We ran into heavy rain during the journey.
Thank you for your efforts during the long journey.
We enjoyed the beautiful scenery during the trip.
during the journey; on the way; while traveling
Used adverbially to describe events or states occurring in the course of a journey. Often appears as 道中で or 道中に.
I met an interesting person on the way.
We took several breaks while traveling.
Before setting off, we prayed for a safe journey.
I traveled together with a friend.
After a long journey, we finally arrived at our destination.
旅行 is the neutral, everyday term for a trip (often for leisure), whereas 道中 has a slightly literary feel and focuses on the journey itself.
途中 means 'on the way' or 'midway' for any process or trip, while 道中 specifically refers to being partway through a longer journey.
Compound of 道 (road, way) and 中 (middle, during). The literal meaning is 'on the road' or 'during the journey'.