This is not a weird question at all! The stars are so important in Middle Earth, and Tolkien put a good deal of effort into making Middle Earth’s astronomy as realistic as possible - by basically mirroring the same constellations we see in our night sky today. The constellations described in the stories are:
- Anarrima: This constellation’s name means “sun border.” Though there’s no official explanation as to which modern constellation Anarrima is, it would be visible in the northern hemisphere. Some astronomers suggest that the name “sun border” indicates that Anarrima is really Gemini. Anarrima was one of the constellations that Varda created just before the wakening of the elves, using stars made from the dewdrops of Telperion, one of the Two Trees of Valinor.
- Menelmacar: “Menelvagor" in Sindarin, this constellation’s name means "Swordsman of the Sky”, and is today known as Orion. Menelmacar was said to represent Turin Turambar, and told of his eventual return in the Dagor Dagorath to kill Morgoth. Another of the early stars made by Varda.
- Remmirath: The “Netted Stars”, this constellation is today known as the Pleiades. The Remmirath was also most likely one of the constellations that Varda created just before the wakening of the elves.
- Soronume: This constellation’s name means “Eagle of the West." Tolkien never confirmed which of the modern constellations this is, but astronomers suggest that it’s likely either Aquila or Lyra. Another of the early stars made by Varda.
- Telumendil: Meaning “Lover of the Stars”, this constellation is a bit of a mystery. Astronomers think that it might be modern-day’s Boötes, but they aren’t sure. Another of the early stars made by Varda.
- Valacirca: This is the most important constellation of Middle Earth. “Valacirca" is it’s Quenya name, and means "Sickle of the Valar.” In Sindarin it’s translated to “Circh i-Mbelain”, and is sometimes called “Ostelen" or "Egedil" - both of which means "seven stars.” The hobbits called Valacirca “Burning Briar”, or sometimes “the Wain”, “the Sickle”, or “the Plough.” And, while it was never confirmed by Tolkien, many readers believe that the Valacirca is the same constellation as “Durin’s Crown”, the seven stars that Durin saw in the Mirromere. Today, this constellation is known as Ursa Major. This constellation was created through the joint efforts of Aule and Varda. Aule was working on making a silver sickle, and when he struck it with his hammer seven sparks flew up into the sky. Varda quickly caught them and set them in the northern sky as a challenge and a warning to Morgoth of his eventual downfall.
- Wilwarin: This constellation’s name means “Butterfly." Christopher Tolkien believes that it is today known as Cassiopeia. Another of the early stars made by Varda.
Beyond these main constellations, Tolkien also identifies several important stars in Middle Earth’s sky, such as:
- Alcarinque: It’s name means “the Glorious”, and was one of the brightest stars that Varda made before the elves awoke, using the dewdrops of Telperion (one of the Two Trees of Valinor.) Today, we know this “star” as the planet Jupiter.
- Borgil: This red star is said to be found close to the constellation of Menelmacar. Astronomers believe that it’s either modern-day’s Aldebaran or Betelgeuse. It was one of the stars created by Varda before the elves awoke, using dewdrops from Telperion.
- Carnil: Another red star, this is actually the planet Mars. It’s another of the early stars made by Varda.
- Earendil: Earendil is not actually a star (see this post for a more detailed discussion), but is the silmaril that the elf Earendil carries through the sky each night on his flying ship Vingilot. Because of it’s extraordinary origins, the star of Earendil is probably the most-loved star among the elves. In today’s sky, Earendil is the planet Venus.
- Elemmire: Meaning “star-jewel”, Tolkien’s notes suggest that this “star” is actually the planet Mercury. It’s another of the early stars made by Varda.
- Helluin: It’s name means “blue”, and this star is part of the constellation Telumendil. Today it’s known as Sirius. It’s another of the early stars made by Varda.
- Luinil: This star’s modern-day equivalent is a bit of a mystery. It’s name means “blue”, leading some Astronomers to suggest that it’s the planet Neptune. But it’s described as a bright light in the sky, and Neptune is so far away that it is barely even visible to the naked eye. Other alternatives are Rigel (which would make Luinil the blue “mate” of the red star Borgil, since both are part of the constellation Orion, or Telumendil), or Spica or Regulus - both blue stars. It’s another of the early stars made by Varda.
- Lumbar: This star’s name is probably connected to the Quenya word for “shadow,” and is actually the planet Saturn. It’s another of the early stars made by Varda.
- Morwinyon: This star’s name means “glint in the dusk”, and is confirmed by Christopher Tolkien to be the star Arcturus. When the elves awoke, Manwe asked Varda to create more stars to give them light and hope. After her great work, as Varda was returning to Valinor, and she accidentally dropped one last dewdrop from Telperion, which became the star Morwinyon. Though it was an “accident”, the elves loved this star a great deal.
- Nenar: This star’s name has something to do with the Quenya word for “water.” It seems that Tolkien originally considered this to be the planet Neptune, but later reconsidered, as Neptune would be too far away to be considered a bright star, as Nenar was described. It’s ultimate identity is unknown.
As you can see, we actually have a good bit of information about stars and constellations. As for astrology, though, there isn’t much information that I know of. I wouldn’t be surprised if many of the cultures placed special meaning on certain stars or constellations (as astrology has been practiced by almost every culture in the “real world”), but Tolkien doesn’t seem to describe this at all. This might be because, as a devout Catholic, Tolkien would consider astrology to be a mildly sinful superstition…
SOURCES: The Silmarillion, LOTR, The Histories of Middle Earth vol. 1, vol. 2, vol. 5 (“The Etymologies”), vol. 10 (“Myths Transformed” and “Index: Star-names”), this article, “Stars of Middle Earth”, on The Council of Elrond, and Per Lindberg’s “Astronomical Objects Above Middle Earth”