The commas are necessary. A version without commas would be appropriate in a context involving several events with distinct anniversaries - not very likely:
This sort of context is rare (if just conceivable by people with reality problems ) so some people might feel that - if the sentence is short enough - the commas don't matter too much. I would disagree.
The event which celebrates its 30th anniversary puts together two bull (male) camels with a female camel on heat nearby.
On the other hand, the event which celebrates its 20th anniversary puts together only one bull (male) camel with a young
female camel who is not on heat 100 metres away, and the event which celebrates its 10th anniversary puts together a
small cat and a huge rat...