The only things other than soap or detergent that will remove oil during washing are extremely hot water (like genuinely boiling!) or alcohol. Neither of these is likely to be more available than dishwashing or hand soap when you're washing out your lunch box in the work or school lunch room.
You might explore whether you can get dish detergent in little packets (like the ones with condiments in them from fast food restaurants); you could bring these with you and be able to properly wash your lunch box and utensils each day.