The phrase "strange satisfaction" is correct and usable in written English.
You may use it when you are expressing a feeling of satisfaction that is unfamiliar, or which one does not understand. For example, "She felt a strange satisfaction when she heard the news of her promotion."
In time I found a strange satisfaction in writing back to these puppy-crazed children, one that I never got from answering the office phones.
Although doctors are devoting their lives to helping people get better, they seem to find a strange satisfaction in seeing a disease take its expected course.
Like the rider on an amusement, I had that strange satisfaction that it was all designed to be scary, to be fun, and would soon be over.
As a free man he wouldn't exist — and so it is with a strange satisfaction that he wakes up in the Village day after day, week after week, now for more than 40 years.
I get a strange satisfaction from getting ideas and processes out of my head/hands and onto the internet.
The project, entitled GrommIt, combines the strange satisfaction of the hole-puncher with a contemplation of the industrial aesthetic.
While nothing in this dusty, low-budget film achieves the pure cinema pleasures of Sandra Bullock swirling end-over-end into the abyss of space, there are some of the strange satisfactions that come from well-shot screen geography.
Hitting open water in a crowded New York City subway car is one of the strangest satisfactions of metropolitan life.
"It is strange the satisfaction people get over tormenting someone.
It also produced a strange kind of satisfaction: The Oscars never get it right.
I woke up with a strange feeling of satisfaction that it would be O.K. if she wins".
