I'm assuming you mean DXC Service, i.e. running Episerver as PaaS in Azure? For custom redirects you can use https://www.iis.net/learn/extensions/url-rewrite-module/url-rewrite-module-20-configuration-reference. You can also redirect domains in Episerver admin by setting up different host names and then chose a primary one that the others should redirect to.
For vanity URLs there is a property on all pages called 'Simple address'.
How are redirects, rewrites handled in EpiServer DXC? Is there some utility that EpiServer provides that is like bitly