Artem, offset is an economics term, look what i have found (explanation in Russian): http://dictionary-economics.ru/word/%D0%9E%D1%84%D1%81%D0%B5%D1%82

Here is an example for offset. I owed my friend $300. Since I helped him build his deck he offset the cost by $70. Now I only owe him $230. It would be odd to say my friend offset the price by $300, because offset is usually used for a less-than-complete amount. You could also say "That traffic on the highway offset my arrival time by 20 minutes". In this sense the time is added. Offset can add or subtract to the total

Okay so, these are quite different. "Make up for" is pretty casual and could be used to show that you are repaying someone: "I'll make up for the hours I missed at work this weekend". "Reimburse" is formal, often to do with officials: "The insurance company reimbursed my television after it was stolen" "Ofset" is the most complicated one, it means when one payment is effected by another, so: "My pension is offset by my widows allowance". That last one is complicated and hard to explain sorry!