Even though, in the comics, Ares has been said to die, there isn't significant proof that they stay dead.
Ares was said to be killed by Wonder Woman, with an Ax, that split his head into two. But in the same source, I found this:
Despite being gone from the mortal world, Ares is still manipulating events to destroy the Amazons. His next plot involves the birth of five male children via five random Amazons. Once they are born he takes them under his wing before Ares is banished from Themyscira both in body and spirit by his father Zeus.
Again, there isn't significant proof that Zeus was killed. One can only assume that Zeus decided to temporarily vanish over a period of time, only to come back at his will.
Greek gods are immortal. They cannot truly 'die'. In order to 'kill' the gods, you have to destroy the significance their domains hold.
For example, if Zeus has to 'die', his domain; the sky and the lightning must hold no significance. That means that when the sky and the lightning are no longer acknowledged and worshipped by the people, only then can Zeus die.
As for the question: Can gods die?
I believe everything has an expiration date. Maybe gods don't just die and turn to dust, but they may be able to transfer their conscience into another body or form, when one form ages or wears out, beyond recovery.
According to mythology, Pan is the one such god that is suspected to have experienced death.
How did Pan die?
Gods cannot die, immortality being an attribute of all divine beings. Yet there have been some exceptions to this rule. One of them is Chiron, who, suffering from an incurable wound, was granted mortality by Zeus. Another is the first Dionysus, who was destroyed by the TITANS. Then on the death of Pan a rumour arose in the first century AD.
Source: Death of Pan
I also came across an article that says:
A dying god, or departure of the gods is a motif in mythology where one or more gods (of a pantheon) die or are destroyed, or where one or more of them departs permanently from their place on Earth to somewhere else.
Source: Departure of Gods
Again, there is no significant proof that gods die and cease to exist. In most cases, they just chose to be unseen, move form one place to another, or transform themselves into another entity.
In my opinion, we cannot say that gods are aliens, or neither can I deny the fact that they might be aliens. But, if you consider Asgard as a place that is not on Earth, then you can assume they are aliens. No harm in that.
The word 'god' is synonymous to a certain higher power that we cannot explain with available knowledge. The fear of the unknown drives us to believe that anything beyond our knowledge is superior to us. Be it aliens or gods.