We find illusions strange. Are the two terms related, if yes, in what sense, I mean more deeply?
No, the two words have different meanings.
It is quite normal to see a mirage in the desert (it is not strange) but it is an illusion.
On the other hand, it is strange that the government has shut all schools due to disease, but it is very real.
Their origins are different too. Illusion is comes from Latin "en-ludare" suggesting "mock, or play at". Strange comes from French meaning "foreign" and ultimately from Latin "extraneus" (extra- means outside)
There is no deep or shallow connection