[Man-of-the-Wold]

Well, with the Elvish variety of "indefinite" if not necessarily "infinite" lifespan, I think the reason JRRT listed Elves as being immune to disease, as well as old age, was more philosophical than biological.

Old age and disease are natural maladies that affect or infect the mortal world. A serious injury, whether physical or mental is an unnatural event that may be too much to overcome.

And, I think one can take this line of thinking and find the biological justification.

The point is that Elves as powerful spirits of the natural world are able to "transcend" the effects of everyday natural forces on their physical bodies. Whether you attribute it to a hypereffective immune system, or more metaphysically to secondary power that negates harmful pathogens, makes no difference.

I tend to go to the latter. Lothlorien is presented as the epitome of Elvish power manifested in the mortal world. The thing there is that no stain exists on any leaf. It is in the subtle lack of flaws that make's it so beautiful. What are stains in a garden? Molds, bacteria, algae. Ecologically, it is not possible to have any type of environment without these entities, and indeed they may still be there, working magic. But they to not appear or destroy in an ugly way. Likewise, Elvish bodies may still enjoy the symbiotic or helpful aspects of microbial interactions, but not the deleterious ones. The Quendi have power over such basic elements, as they can make goods out of fibers with incredible, but non-technological attributes.

As for Aredhel, I would not think that a powerful toxin, devised by Elves, is necessarily comparable to a pathogenic infection. The latter has to happen before there is disease. The direct introduction of a tissue-destroying substance, seems comparable to massive trauma that can simply not be repaired without instanteously overcoming basic structural laws of existence. It is interesting that JRRT chose to placed grief and extreme psychological distress in this same category.

Also, of interest is how Men are in some ways "hardier" than Elves. One has a picture, that while Elves are more able to ultimately survive greater suffering or deprivation, that Men for limited period times are at least more "willing" to endure physical hardship. The reasons for this are perhaps threefold:
1. Men, and especially the Edain, while not always taller are larger and physically stronger than the average Elf. So, partly, it is a matter of stature.
2. With their short lives, Men are perhaps more willing to take risks and put in on the line. Ironically, it is the indefinite life that may be the more precious.
3. Men have the ability to create beyond the Music of Ainur which is fate to all else. This is not really a matter of hardiness, but may explain how Turin, Tuor and others were able to rise in such esteem among the Elves that they became leaders unto them.