All of the three words could be verb and noun.
安排arrange/arrangement
To arrange resources (time, human etc.)for a specific work,event or a period of time.
例句:
这是对春节期间的放假安排。
This is the scheduel of the Spring Festival holiday.
老板安排小王去联络客户。
The boss let Wang to contact client.
计划 plan
A relatively compelete and considered plan that include the goal, method, shedule etc. As a verb it is more formal and used in written Chinese.
这是下一学期的学习计划。
This is the study plan of next term.
政府计划建设一座医院。
The government plans to build a hospital.
打算 intend to do/intention
It is more casual and informal. For someone intend to do something or just think about to do something.
我打算明天去书店。
I want to go to a book store tomorrow.
她没有去工作的打算。
She does not have the intention of working.