A320 Captain reported a 'burning plastic' odor during descent which resulted in the entire flight crew experiencing physiological symptoms. After a safe landing; maintenance requested and flight crew was referred for medical evaluation.

Narrative

During flight from ZZZ to ZZZ1 on Aircraft X we experienced a fume/odor event that required 4 of 5 crewmembers to be evaluated by paramedics upon arrival. We actually had 2 events; the first of which was on takeoff; and the second started during the descent to landing in ZZZ1.The first odor issue was brought to my attention after signaling that we were above ten thousand ft. The Purser called to tell me that they had an odor in the back that smelled sort of like burning plastic but they weren't really sure. I had the flight attendants seated at the time due to turbulence and weather on departure. Since we had cleared the weather and had only light turbulence at the time; I had the flight attendants get up and investigate to see if they could find the source being mindful to also carefully check to see if there were any hotspots in areas they thought the smell might be coming from. They reported back a few minutes later that there was no smoke or hotspots and that the odor seemed to be dissipating. We lowered the temperature in the cabin and set the pack flow to HI and by the time we reached cruise the smell was mostly gone and continued to go away. No crew or passengers reported feeling ill at that time; and while the odor was noticeable at first it did not seem over-powering or dangerous; so with conditions improving and no way to know what the smell was; we elected to continue towards the destination knowing that better weather and suitable alternates were ahead of us should they be needed. The odor was gone at cruise and did not return until we were in our descent for landing.After we started our descent; the odor returned when the power was brought back to idle. It was first noticed in the cockpit as the same smell from before and then a few minutes later the flight attendants said they could smell it near row 26. The more we descended; it seemed the odor increased. We were close to ZZZ1 at that point so we continued toward the airport and landed with no issues. As we taxied to the gate; I stated to the First Officer that the smell was starting to cause my throat and tongue to feel irritated and I felt like I might be getting light-headed. It was at that time that the First Officer told me that he was also starting the feel sick. By the time we finished that conversation; we were pulling into the gate. After parking; we shut down the engines and opened the cockpit windows and door after completing our checklists. I checked in with the Flight Attendants to see how they were doing. They informed me; that they also were feeling tingling in their throats as well and one said she was light-headed. I inquired if any passengers reported feeling ill and wanted to be seen by paramedics and I was told there were none.I notified Maintenance Control of the issue and told them I was writing up the plane for the odor/fume issue as we deplaned. I got all of the crew off of the airplane and I then contacted the Operations Manager; who was great and very helpful. He advised me to call Medlink which was my next call where I obtained the phone number for Employees which I provided to all the other crewmembers. I had them individually call and get evaluated on the phone by Medlink. I was advised that based on my condition that unless I did not continue to improve; I did not need to see a medical professional. All 4 of the other crewmembers were advised to be seen by paramedics which they did. I continued to monitor how my crew was doing and provided them all with my personal phone number and email; spoke again with the Operations Manager; filled out the Airbus Smoke/Fume/Odor form for maintenance; and interacted with ZZZ1 Operations.I believe that there are some insidious things that occurred during this event that pilots and flight attendants should be aware of. We have odor events all the time on our aircraft and 99.99% of the time they go away with no issues and we continue on. We become biased to believe it is no big deal; andgenerally the first thought isn't to get out the Smoke/Fumes/Odor Checklist. Many believe they must have burned something in the oven or the airplane was de-iced and it's a residual smell or something like that. We don't usually think about how the longer-term breathing of an odor or fume will affect us even if the smell is tolerable because we may be pre-occupied with flying the aircraft around weather or preparing to land. We are always taught to fly the airplane first so it's possible that we might not react as quickly as we would like. We sometimes don't share how we are doing with our fellow crewmembers; I wish I had known my First Officer was starting to feel sick in the air. I was flying and concentrating on landing and should have asked him how he was doing; but I did not. I have a very sensitive sense of smell; so I thought the strong odor was more me than anything; We need to remember that in the future should something like this occur again; we need to open up a conversation much sooner and ask about how each person is feeling. We as pilots need to bring the Flight Attendants more into the conversation. While I pride myself on communicating with our Flight Attendants; there is always room for improvement. While I was getting feedback from them on how things were going in the cabin; I probably could have asked more and better questions to include asking how they were feeling. I didn't know until after we deplaned that at least one flight attendant felt light-headed.