Pandemic already implies disaster. A pandemic is a kind of disaster. And disaster implies effect--it has to, otherwise it isn't much of a disaster. So what you have is a sentence where the subject noun has to go looking for a verb to justify its existence. And that's why you're tripped up by auxiliary verbs and matters of thesaurus.
(Sometimes you have to mark time at your keyboard to get through in the academy, I get it. To your credit, this problem is only so obvious because you picked strong noun. Maybe tee off farther from the green if you want to whack the ball with a couple of different irons on the fairway? Use a subject like the situation with COVID19? Or just skip it and get to the meat of your paper.)
To your question I would say that those three words are all interchangeable to economists and academics because these aren't particularly literate or deep thinking groups of people in general anymore. But to anybody who's paying attention yes, they're different words. I'm not sure what's accomplished by me explicating the dictionary (you have to read it for yourself) but I'll give it a shot:
Impact this is the language of contact, violence. An appeal to physics. (Because it sounds so concrete, the word is systematically misused by bullshit artists in business, politics.)
Influence is the language of hydraulics, magnetism. Fluid/flow/confluence/fluency. Also an appeal to physics, but the source of the energy could be farther away. (This might be seen as weak or wishy-washy language, since is often cleverly used to imply direct causality where there is none.)
Effect derives from ex-facere = to do/make, and suggests a result with some finality, clarity. (Again, it's a term that's been systematically misused to do an end run around making an argument about how something causes something, to begin by discussing the thing that happens as an outcome.)
You can mostly go down the list like this. Consequence like effect, a term implying certainty, logic. Con =with + sequence. Repercussion from French "to hit back". Thrust (same thing).
Good, exact words for concrete matters will always be used by those who don't have a good or exact, or concrete point to make, and end up sounding meaningless.
This is not really a concern in the academy or for the media if you want to sound smart. But if want to make sure you're thinking and writing clearly, or if you are not writing for our luminary intellectual classes, you should make your case with your case, and open the door to pathos gently, using understatements, rather than synonyms for doom and ruin.
Some examples of understatements:
"Houston, we have a problem." -- Apollo 13 to Mission Control.
"It’s a scratch, just a scratch." -- Mercucio, Act I, Romeo & Juliet
"I'm just going outside..." -- Lawrence Oates
That sort of thing. Aesthetics are of course subjective, but in my opinion you'll get more mileage out of a term like painful, or worrisome or troubling.
This is a long way of saying they're all fine, and don't overthink this if it's for school.