In context they could all mean the same thing, or they could be different.
"Pre-requisites" are likely to be applied to individual courses at a college. The pre-requisites might be other college courses, grades in tests, or general qualities that are needed.
The prerequisites for the Calculus 2 course are either a passing grade in Calculus 1, or a high school mathematics certificate at an advanced level. In addition, students require a willingness to work hard and must commit to finishing all the homework by the required deadline.
"Entry requirements" would be about something that you enter. We talk about entering a college or university, but we say "you take Calculus" (we don't say "you enter calculus"). Thus it would make sense for "entry requirements" to be the grades that you need to enter the school, not particular pre-requisites for the courses at the school.
The Entry requirements for Law at Oxford University are Three A-levels, two of which must be at A* grade and the third can be no lower than A grade.
"Course qualifications" is not a phrase I've heard used. Without other context, I'd assume it meant the qualification that you earned on completing the course.
Course qualifications: The Introduction to Computer Use course will introduce the basics of word processor and spreadsheet design. This course is a pre-requisite for the Computing in Business course. In addition, all students who complete the course will also qualify for the ECDL certificate.