Purchasing Group and Purchasing Organization 

How can we create a pur org at enterprise level ?

SPRO > Enterprise Structure > Materials Management > POrg > New Entries

If we create a purch org at plant level, is it necessary to assign that purch org to the company code ?

There is no option to create a Purchasing Org at Plant, it is an independent entity, it can be assigned to a Plant or a company code or to the both.

Is it necessary to assign purchasing group to the purchase org ?

Is there any procedure by which a purchasing group (or many purchasing groups) could be assigned to a purchasing organization? 

There is no such configuration exist in SAP to link Purchasing Org to Purchasing Grp.

1. Purchasing organizations that procure for several company codes (contract management) are not assigned to one company code. They can procure for the any company code.
2. It is not mandatory to assign Pur org to the company code.  If you want to have company code specific purcahsing organisation then you have to assign it to the company code.
3. You cannot assign purcahsing organisation to puchasing group.

Purchase organisation is created by customizing
SPRO-Enterprise structure-Definition-MM-Maintain Purchase organisation.

Plant - purchasing organization/company code
In the SAP system, a plant must be assigned to one or more purchasing organizations. 

Furthermore, a plant must always be assigned to a company code. 

Purchasing organization company code
A purchasing organization can (but need not) be assigned to a company code.

If you do not assign a company code to a purchasing organization, the latter can engage in procurement operations for every company code.  A prerequisite for this is that the plant for which procurement is carried out is assigned to the purchasing organization. 

Purchasing group need not be asigned to a purchase organisation.

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