Invasion is a much stronger word - unwanted guests intrude, yet countries invade each other.

Consider:

I would normally say “invasion of privacy”, rather than “intrusion of privacy”, even though the meanings are similar. I also think of “invasion” in terms of the use of force, such as the invasion of a country. I would use “intrusion” to say things such as “Pardon my intrusion into your conversation” or “there were intruders at our party last night.” An intruder can also be someone who is trespassing on private property, usually with the intention of harm to the premises or persons therein.

Intrusive is similar to someone having a peek at your phone while you're using it. that's intrusive.

Invasion is a full blown out action, the Brits have invaded/colonized most of the world. (as an example.)

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