"In order that" and "so that" mean the same thing, but in the US we usually don't say "in order that". We would usually say "in order to". These are the same: I go to work in order to earn money to pay my bills. I go to work so that I can earn money to pay my bills. I think "in spite of the fact that" and "despite the fact that" also mean the same thing. I've never recognized the similarity between "in spite" and "despite" before. We don't use the word "spite" very often. "Despite" is much more common. In my opinion, the word "spite" is often used to imply a disagreement or conflict. When you do something "out of spite" you do it to harm someone, even if there's no benefit to you or if it also harms you. I won the race despite the fact that my foot hurt. I told the teacher he cheated out of spite. I hit his car with my car just to spite him, despite the damage to my car. When you say you do something "out of spite" you are admitting it was petty and shameful.