What is the maximum lateral deviation allowed on an RNAV route?
4 nm from centerline or 8nm total width of airway.
You are not required to instantly turn when transitioning between airways.  Required navigational precision for most enroute segments is 2 nm.  Being conservative and always assuming an operational error of 2nd means any observed deviation of more than 2 nm is a red flag.

Intentionally deviating within the course width is not prescribed within the regulations, but then there's no regulation prohibiting or allowing fly by (fly over is sometimes mandated).