This question is a little outside my scope as it relates more to data structures than storage.
Of the four you mention, I do not think the "network data model" is very useful. There is too much ambiguity to the idea.
The object data model implies such things as inheritance for objects that have child parent relationships.
The relational data model is based on the relationship between data in tables made up of rows and columns. Advanced descriptions of the relational model discuss normalization of the data to ensure there is no redundancy and possibility for inconsistent (stale) data.
The hierarchical data model implies relationships of data in a database that is accessed through defined hierarchies, as opposed to tables.
This was first published in August 2001