What are the possible way by which external system can insert/update multiple records in salesforce without writing any apex webservice. If webservice is required how it can be implemented. Please provide a sample code.
See the treesave API pilot:
It lets you save records in hierarchy via the rest API. https://developer.salesforce.com/docs/atlas.en-us.api_rest.meta/api_rest/resources_composite_sobject_tree.htm
One of the things that's been omitted from the other responses to this question is that multi-record updates typically involve the use of some kind of wrapper class. So, even if someone has your WSDL, unless their service will work with the standard Apex Web Services classes (using your WSDL), any kind of custom service will involve either some kind of "middleware" on their end or creating a class that can process (or "accumulate") the inbound call into a list that Apex can parse/handle via what's essentially a wrapper class. That's the essence of how outbound multiple records are sent, so code that's essentially the equivalent needs to be configured to handle the records as they arrive on this end.