Лето (summer).
[Падеж: единственное, множнственное]
И.: лЕто, лЕта or летА
Р.: лЕта, лЕт
В.: лЕто, лЕта or летА
Д.: лЕту, лЕтам
Т.: лЕтом, летАми (or лЕтами?)
П.: о лЕте, о лЕтах

Год (year).
И.: год, гОды or летА
Р.: гОда, годОв or лЕт
В.: год, гОды or летА
Д.: гОду, годАм or летАм
Т.: гОдом, годАми or летАми
П.: о гОде, о годАх or о летАх

The plural лето is almost never used. It is hard to make up a phrase with it uncontaminated by the plural год. I cannot think of any example of летАм and о летАх, which I would not perceive as the form of plural год.

Also the this word might be (indirectly?) affected by the general process of shifting the plural forms of some words to the form with the stressed final -а. Like профЕссоры -> профессорА, кАбели -> кабелЯ, and so on. The shifted forms usually first appear in the professional speech, then after some time they may become accepted by the rest of the society. So the form with the stressed -а has the tint of being a professional term. I mean when one uses the new form of the word (when both forms are possible) it sounds a bit like if he's a pro, however this is not very strong. The last two sentences is only my own opinion.

Предыдущие два лЕта (р. п., ед. ч.) были не такими жаркими.
Предыдущие пять лЕт (р. п., мн. ч.) были не такими жаркими. (This one is very unnatural and ambigious because год -> лет (р. п., мн. ч.) is far more common)
Это лЕто (и. п., ед. ч.) жаркое. ЛЕта (и. п., мн. ч.) теперь жаркие. (ЛетА is also possible, but it would feel a bit like you know everything, as I've already said.)
Зимы и лЕта (и. п., мн. ч.) случаются каждый год. (летА is possible and seems as (un?)natural as лЕта)
И зимы, и летА (и. п., мн. ч.) бывают каждый год. (I like летА here better, because 1. лЕта sounds like лЕто, and 2. rhythmically it seems to be easier to pronounce)
Рассказывать о зимах и лЕтах (п. п., мн. ч.), прожитых не важно где. (Also this is alredy rather unnatural, летАх would be even more unnatural here.)
Нашим теперешним лЕтам (д. п., мн. ч.) не позавидуешь. (Unnatural, летАм is much more unnatural to me.)
На экваторе не бывает ни зим, ни лет (р. п., мн. ч.). (Can appear in free speech, as after one's said зим he has to continue with Genitive case.)
I'm tired of thinking of exmaples, so Accusative and Instrumental would go without them.

In all the examples above plural лето feels like a stupid word. Foreigners should never use it.

(Corrections are appreciated.)