They are similar because the Norsemen and the Greeks were distant cousins, and their cultures derived from the same ultimate source: Proto-Indo-European, the very ancient "mother" culture which dwelt (probably) on the Eurasian steppes in the 4th and 3rd millennium BCE, innovated the plow and the domesticated horse, and spread into every corner of the then-known world, east to the deserts of China, southeast into India, southwest into the Caucauses and the Middle East, and westward into Europe and the Mediterranean littoral. The PIE culture birthed those who would eventually develop to speak many ancient and modern languages, including Norse and Greek.
Virtually everything we know about PIE culture is derived from her daughter cultures, especially the daughter languages. By comparing the languages which survive, we can reconstruct aspects of the PIE language, and from there infer aspects of PIE culture. This is called historical linguistics.
This is what we learn when we examine various daughter cultures' words for divinity: PIE associated gods (plural) with the sky, the world up there, and we find a word associated with this very basic concept in virtually every one of the dozens of daughter languages. The PIE root was diw/dyu"sky, light" and we find that word or its derivatives associated with a sky god everywhere the Indo-Europeans roamed (for example: Vedic devá-; Latin deus; proto-Germanic tīwaz; Old Irish día; Mycenaean de-wi-jo). Some languages brought alternate, but still related terms. This includes the Norse of your question, who do not cooperate and give us Old Norse goð, a cognate of that PIE root but not the same word. We see it also in Old High German got, English ‘god’. It seems to be a neuter collective term for the gods as a group, rather than the (usually male) sky god in particular. Greek also, by the way, does not cooperate, giving us theos. Still, all these examples are related to each other directly in their origin, and their subsequent developments as far as mythology are ultimately from the same PIE source.
Some other commonalities: with very few exceptions, PIE gods are immortal, in direct contrast to those who dwell on the Earth (humans, mortals). They are male and female, and there is a strong association with "mother" gods and their offspring. And there are often male-female pairs, as you have noticed. They are associated with domains (sky, fire, water, love, liminal space, animals/hunt, motherhood, death, justice, ruling power, etc).
The similarities you detect are due to their common origin, but we don't have a primer of Proto-Indo-European myth to start us off. We have to reconstruct it as best as we can, from what is left, and that is a very messy and difficult process. Here's an example, quoting M.L. West:
"Of course, many of the purposes for which people require gods are universal. If we find a god of healing here, there, and everywhere, we cannot assume them to be historically connected unless they show more distinctive identifying features. Nor is it remarkable if many peoples have a god of war to help them to victory or defend them against defeat; war is a critical event, and success must depend on divine support as well as military prowess. We find war-gods, for instance, among the Indians (Indra), Greeks (Enyalios, Ares), Scythians (‘Ares’, Herodotus 4. 62), Romans (Mars), Gauls (‘Mars’, Caes. Bell. Gall. 6. 17. 2–5), Germans (‘Mars’, Tac. Germ. 9. 1, Ann. 13. 57, Hist. 4. 64), and Goths (‘Mars’, Jordanes, Getica 41). Perhaps it is more noteworthy when the war-god is also an agrarian deity, a protector of the fields, as is the case with the Roman Mars, the Celtic ‘Mars’ Teutates, and the Slavonic Svętovit. Enemy action is of course one thing that the fields need to be saved from, but these gods are also concerned with successful harvests and with protection from blight. As for healing gods, they do occur everywhere, but again there are sometimes other coincident features. The Greek Apollo, a rather complex figure, has probably taken over the characteristics of more than one older divinity, including the healer Paiawon (Paieon, Paion, Paian). He has points of contact on the one hand with the Indian Rudra, on the other with Celtic and Germanic deities. His power over sickness and health is dramatically portrayed in the first book of the Iliad, where he first shoots his arrows to bring plague upon cattle and men, and then relieves it in response to prayer. The image has striking parallels in Ugaritic and the Old Testament. But Rudra too is pictured in the Veda as an archer whose missiles send disease and death upon humans, cattle, and horses. Prayers are directed to him imploring him to spare his worshippers and their animals. He is said to have a thousand remedies at his disposal, and a healing hand."
This is from the very excellent: M.L. West, Indo-European Myth and Poetry (Oxford, 2007), from chapter 3 "Gods and Goddesses."
There are two basic answers to this. One is that at least one of the major authors of our sources for Norse literature, Snorri Sturluson, was familiar with Greek myth, and since the sources were written down by Christians, in Christian times, there was almost certainly some indirect influence. /u/Platypuskeeper has a great answer dealing with the issues of Norse mythology sources here.
But that's only half of the story. Both Norse and Greek religion belonged to a broader group known as Indo-European Religions, and the underlying oral traditions thus have shared roots not only with each other but with Roman, Celtic, Slavic, Iranian and Indic religious traditions.
The Proto-Indo-Europeans were a pastoral people who likely dwelled in what is today Eastern Ukraine about 6000 years ago. Sub-groups gradually split from them; apart from the aforementioned ones, Albanian and Armenian are also Indo-European languages. When looking at archaic languages such as Old Persian, Old Latin and Sanskrit, it is easy to find cognates - a simple, basic one is Latin "Mortalis" and Sanskrit "mrta", both meaning "mortal" or "man". Another one is Latin "ignis" and Sanskrit "agni". Much can be learned about the Indo-Europeans merely by reconstructing their vocabulary.
About the parallells and broad themes of Norse and Greek religions, I would not necessarily subscribe to the examples you give. Linguistically, Zeus corresponds to Tyr, going back to the PIE god Dyeus Phter, or "Father Sky", but Zeus appears influenced by Near Eastern storm deities like the Ugaritic Ba'al or Yahweh as well. The notion that the gods have various domains is not really particular to Greek or Roman myth either.
However, the notion of Fate being important and the existence of three Fates is probably a correctly identified parallel. The idea of a "natural order of things" can arguably be identified in the Indo-Iranian concept of "Asha"/"Rta" as well, and things coming in triplets and twins and twins of triplets is recurring as well. Other features include a hero or warrior-god who fights a monstrous serpent with a blunt weapon (Hercules/Thor) which is also found in other religions (Indra in Vedic religion, Thraetona in Zoroastrianism) and in fact has spread to many non-Indo-European traditions as well.
There are many particular themes and stories one can find various connections between (including less obvious things like patriarchy, an ideal of social hierarchy, et cetera) but the basic answer is that some of the similarities reflect shared origins.
The go-to book for the Proto-Indo-Europeans is "The Horse, the Wheel, and Language" by DW Anthony.
Could you please specify in what aspects they are similar?
