Incursion and Invasion have military links, Incursion would be brief and limited in scope, invasion is more full on long term. Both terms imply a subtle but a conscious choice in the crossing of the barrier, while intrusion is more neutral in attributing agency to the action.
Runway incursion is a technical term defined by the ICAO:
> Runway incursion. Any occurrence at an aerodrome involving
the incorrect presence of an aircraft, vehicle or person on
the protected area of a surface designated for the landing
and take-off of aircraft.
OP only quoted "Invasion", he did not reference it as "Runway Invasion" perhaps he meant the ICAO term, perhaps he took issue with the term invasion. I assumed he meant the latter, How would we know for sure?
Ambiguity while correcting someone else is not ideal.
Incursion and Invasion have military links, Incursion would be brief and limited in scope, invasion is more full on long term. Both terms imply a subtle but a conscious choice in the crossing of the barrier, while intrusion is more neutral in attributing agency to the action.