Direct Material:

• Direct materials are those materials which are easily identifiable with the cost of production.

• Direct materials can be conveniently measured with the cost of product.

• Direct materials are part of the finished products.

• Direct materials are part of the prime cost.

Indirect Material:

• Indirect materials are those materials which can not be easily identified with the cost of production.

• Indirect materials can not be easily measured in cost of production.

• Indirect materials are part of the overheads.

• Indirect materials are part of the factory cost.

Direct Labour:

It is the type of labor which is directly related with the manufacturing of product in factory

E.g. : - Like people directly working on machines for production of goods.
 

Indirect Labour:

It is the type of labor which is labor in nature but do not directly relate with the production of goods or without which the product can still be made

E.g :-  Like Supervisor in factory who supervise the workers working on machines to produce any product.

Direct expenses :

They are those expenses that are levied during
the production of goods.

E.g :- wages, frieght, carriage inward, etc
 

Indirect expenses :

These are are those expenses that are levied
after the production of goods and services.

E.g :- Advertising, Salary and office expenses. etc

While the difference between from COST CENTRE & COST UNIT, i could not explain properly, so got it from some website and hope that stands true :

The DifferenceBetween Cost Centre and Cost Unit.

Cost centres are the smallest segment of activity or area of responsibility for which costs are accumulated or ascertained. I.C.M.A., England defines cost centre are the 'allocation, person or item of equipment for which cost may be ascertained and used for the purpose of cost control'. Cost centres are the natural division of the organisation in to convenient units for the purpose of cost ascertainment and control. These are the department of the organisation, but sometimes a department may also contain several cost centres.

Cost units is device for the purpose of breaking up cost in to smaller sub-divisions. I.C.M.A., England defines, cost unit is 'a unit of quantity of product, service, or time in relation to which cost may be ascertained or expressed'. Ordinarily cost unit is the expression in the form of count, weight, dimension etc. Cost unit is the unit of measurement of different types of products. For example, ton in case or coal, Yards in case of cloth, Liter in case of petrol etc.