To me the nuances lies in the intent/the degree of hostility. Intrusion can often be stealthy and/or unvoluntary, and can be boiled down to going somewhere without the owner's permission, whereas invasion has no intention to hide and usually implies a takeover of power on the invaded place by the invaders (although language is flexible and uses can vary, this is just my rough sense of what the words evoke).

they differ in seriousness. An invasion is usually associated with something very serious or dangerous. Like a thief invaded my home. We have an ant invasion, the army invaded our country, aliens are invading our world. An intrusion(intrude) is similar in concept but less serious. It’s similar to an interruption or interfere. Like if you’re trying to have a romantic date with your wife or so and then your mother in law invites herself to join you. You can call her an intrusion or say she’s intruding on your date. You can also use invasion in this case only if you’re wanting to be dramatic or emphasize how serious her intrusion is.

Both mean the same thing but intrusion is more polite/ less personal. For example, an intrusion is an unwanted guest inviting themselves over for tea, while someone can invade your privacy by looking through your phone.

hello junji how are you?