The procedure would likely be the same as any other medical emergency: get the plane on the ground (which is a thing that pilots are good at doing, and have the training and skills to do) so that the medical crews can handle the medical emergency (which is a thing that pilots are not good at doing, and have neither training nor skills to do)
The initial radio call might be something along the lines of "Mayday mayday mayday, Oceanic 201 requesting immediate vector to LAX for a medical emergency, multiple passengers"
- "Mayday" indicates several things all at once.
- "Everyone else currently on this radio frequency, shut up."
- "I am in the middle of an emergency, therefore I am now the most important person in the sky."
- "I will do whatever I need to in order to keep this plane safe. Air traffic controllers, you will get everyone else out of my way."
- Saying it three times has no relevance other than to make sure that it's heard and the number three indicates distress in general.
- "Oceanic 201" is the callsign of the aircraft.
- "Requesting" is used to tell ATC that the crew requires action from them, in this case a vector to a suitable airport.
- "for a medical emergency, multiple passengers" prepares the emergency crews for whatever situation they're about to have dropped in their laps.
For further examples of cockpit-to-ATC communication under critical circumstances, you might find it helpful to read the cockpit voice recorder transcript of United flight 232, or other in-flight emergency transcripts.