Wikipedia articles on social norms, social groups, and social roles provide a reasonable starting point. Standard sociology textbooks will cover this material.
Let's think of the example of a family.
A particular family with two parents and two children is a social group. We could say that there are social roles for parents (e.g., around setting boundaries, providing a safe environment for the children, etc.) and social roles for children (e.g., learning, having fun, being respectful to parents, etc). We could also describe social norms that operate in the family (e.g., around interaction patterns, styles of dress, eating habits, etc.).
Difference between "Social Roles" and "Social Groups"
Groups are sets of people. Roles describe a set of features of a position in a social structure. Roles are not a person, but represent a position filled by a person in a social context.
E.g., A family is a group; parent or father or breadwinner is a role.
Difference between "Group Norms" and "Social Norms"
The term "group norms" is often used to describe the norms (i.e., the expectations and typical ways of acting) that operate in a particular group or set of groups.
E.g., the norms in a particular family or in a set of families in a particular community; the norms in a particular work team
I see the term "social norms" as more general. When used in the context of describing expectations and typical human behaviour, all norms are "social". Thus, social norms can apply to social contexts that transcend any one group (e.g., face the door when waiting in an elevator; don't laugh when attending a funeral service).