While there is no official retail release, the dedicated homebrew community has explored several "workarounds" to bring the Omori experience to the handheld:

For those who just want the aesthetic, fans have created high-quality OMORI 3DS themes that include custom music and icons for the Home Menu. Understanding CIA Files and Modding

For users with custom firmware (CFW), software is typically installed via files. 3DS:Installing software - Hacks Guide Wiki