Connections between Krishna and extraterrestrial life
First, Krishna is the origin of all incarnations and expansions, including the three Vishnu avatars. The first one, Mahavishnu, creates the total material energy known as the Maha Tattva. The second, Garbhodakshayi Vishnu, enters into all the universes to create diversities in each of them. The third, Kshirodakshayi Vishnu, is diffused as the all-pervading Supersoul in all the universes and is known as Paramatma, Who is present even within the atoms.
Here are just two of the many verses that explain the original position of Lord Krishna:
"All of the above-mentioned incarnations are either plenary portions or portions of the plenary portions of the Lord, but Lord Sri Krishna is the original Personality of Godhead. All of them appear on planets whenever there is a disturbance created by the atheists. The Lord incarnates to protect the theists." ( Srimad Bhagavatam 1:3:28)
"Krishna, who is known as Govinda is the Supreme Godhead. He has an eternal blissful spiritual body. He is the origin of all. He has no other origin and He is the prime cause of all causes." (Brahma Samhita, 5:1)
As far as who is an alien and who is not:
Actually everyone is an alien in this material world. We all belong in Vaikuntha, the spiritual world. Each living entity is a spiritual spark, coming from Krishna and originating in Vaikuntha. Due to desire to enjoy the material world separate from the Lord, some souls come here to this earthly realm. This is a very alien atmosphere for us. We're meant to live in an eternal, blissful state, but find ourselves in a place where everything is temporary and full of misery.
When Lord Krishna appeared here five thousand years ago, He came in His original form. Lord Krishna's body is spiritual. This means it is eternal (sat), full of knowledge (cit) and full of bliss (ananda).
Each of us is meant to have a body qualitatively the same as Krishna's, and to live in a spiritual atmosphere, where our mood of service to Krishna allows us to experience our natural, spiritual qualities. Instead we come to this alien place, looking for cheap thrills. We settle for a body made of blood, pus and other horrible things and where everything is constantly getting old and dying, and hopes for happiness are destroyed by the temporary nature of the things we aspire to enjoy.
In one sense Lord Krishna was also an "alien" when He came to the earth—because this isn't His original residence—but in another sense everything is His, and comes from Him. He's the proprietor of everything, so He can go wherever He wants, and appear however He wants—either via flower airplane, the speed of mind, or innumerable other traveling options. And when He travels He's not subject to the discomfort of the place He's visiting, He simply brings the wonderful spiritual qualities and atmosphere of His place with Him!
You're also correct in saying that during the Mahabharata war there were aliens fighting with Krishna and others on the battlefield. Earth isn't the only planet in this material realm. Actually there are billions of galaxies in the material world—which is only a small section of the entire spiritual realm—and in each galaxy there are many, many planets. Some are heavenly, some are hellish, and some are in-between. On each and every planet there are living entities with different bodies. Many residents of these planets are very advanced in yoga and other mystical sciences, so they can travel at will to different planets. In the Mahabharata war there were visitors from higher planets assisting both personally and by allowing warriors to use their weaponry.
However, it's also a fact that wherever in this material world one is, one is an alien; because our original place is in the spiritual world with Krishna!
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