Games like The Odyssey
Games like The Odyssey include Chants of Sennaar, There Is No Game: Wrong Dimension, Machinarium, Gorogoa, and Return to Monkey Island. We matched them by the tags players give The Odyssey on Steam (Point & Click, Adventure, Mythology, Casual, and Education): closest matches first, and among equally close ones the better-known games.

Chants of Sennaar
Shared: Adventure · Point & Click · Puzzle

There Is No Game: Wrong Dimension
Shared: Point & Click · Adventure · Puzzle

Machinarium
Shared: Point & Click · Puzzle · Adventure

Gorogoa
Shared: Puzzle · Point & Click · Casual

Return to Monkey Island
Shared: Point & Click · Adventure · Puzzle

Old Man's Journey
Shared: Adventure · Story Rich · Casual

Lost in Play
Shared: Point & Click · Puzzle · 2D

Deponia
Shared: Point & Click · Adventure · Puzzle

Carto
Shared: Puzzle · Adventure · Story Rich

Broken Age
Shared: Point & Click · Adventure · Story Rich

Fran Bow
Shared: Point & Click · Adventure · Puzzle

The Room
Shared: Point & Click · Puzzle · Adventure

Scribblenauts Unlimited
Shared: Adventure · Casual · Puzzle

Servant of the Lake
Shared: Adventure · Point & Click · Puzzle

Sally Face - Episode One
Shared: Story Rich · Adventure · Puzzle

Rusty Lake Paradise
Shared: Point & Click · Adventure · Puzzle

The Room 4: Old Sins
Shared: Point & Click · Adventure · Puzzle

Slime Rancher
Shared: Adventure · Singleplayer · Exploration

Morphopolis
Shared: Point & Click · Puzzle · Adventure

Storyteller
Shared: Point & Click · Adventure · Puzzle

Hidden Folks
Shared: Casual · Point & Click · Puzzle

Papers, Please
Shared: Point & Click · Singleplayer · Puzzle

The Tiny Bang Story
Shared: Point & Click · Puzzle · Casual

OneShot
Shared: Story Rich · Puzzle · Adventure