Canon 77D has a Canon EF/EF-S lens mount and currently there are 333 native lenses available for this mount.
The latest released lenses that are compatible with the 77D are the Carl Zeiss Makro-Planar T2/50, the Tokina 35mm f2.8 Macro DX and the Canon 50mm f2.5 Macro.
Canon 77D doesn't have a sensor based image stabilization system but
113 of these lenses already comes with optical image stabilization.
Since Canon 77D has a APS-C sensor, it has a focal length multiplier of 1.6× so you have to multiply lenses original focal length with this multiplier to find the Full Frame equivalent focal length of the lens when mounted on 77D.
You may also also be interested in these:
Canon 77D Lenses with Image Stabilization
Canon 77D Lenses with Weather Sealings