While exploring in weirdest side quests in Oblivion. However, newer players might not know why these quests are worth doing and how to find each of the shrines.
Within Elder Scrolls lore, there are 17 powerful Daedric Princes, who will offer boons if the correct offering is placed on their shrine and a quest is completed. In Oblivion Remastered, there are 15 shrines to find, with Mehrunes Dagon and Jyggalag heavily involved in the main plot and the Shivering Isles DLC, respectively. If you're planning to seek out the favor of all the Daedric Princes, it's worth noting that while some of the Daedric Shrines can be stumbled upon easily, others are definitely harder to find.
15 Azura's Shrine - Requires Level 2
Azura's Offering: Glow Dust
Azura’s Shrine is to the north of Cheydinhal, high in the mountains, making it a little tricky to get to. In order to get Azura's quest, you'll need to leave an offering of Glow Dust either at dusk or dawn, between five and seven, either in the morning or the evening.
During the main quest, Martin will suggest Azura’s Shrine in order to gain a Daedric artifact.
Glow Dust is collected from dead Will-o-the-Wisps, and luckily, some will appear around Azura's Shrine at dawn at dusk to help you get some. Azura requires you to be at least level two before she will accept the offering.
14 Sheogorath's Shrine - Requires Level 2
Sheogorath's Offering: Lettuce, Yarn, & Lesser Soul Gem
Sheogorath's Shrine is almost exactly between Bravil and Leyawiin, west of the road in a forested area. To speak with the Daedric Prince of Madness, you'll need to offer a head of lettuce, a lesser soul gem, and a spool of yarn, at any time of the day or night.

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All of these items are very easy to find, and so long as you are at least level two, Sheogorath will offer his side quest. Dialogue with Sheogorath will change depending on whether the main questline for the Shivering Isles has been started or not.
13 Namira's Shrine - Requires Level 5
Namira's Requirement: Personality Attribute Must Be 20 Or Less
Namira is the Daedric Prince of Hunger and is often worshiped by cannibals, and her shrine can be found east of Bruma. Unlike Azura or Sheogorath, Namira will not speak to anyone she deems too 'attractive' and will only respond to those with a Personality value of 20 or less. I've found the best way to lower Personality in Oblivion is to drink alcohol, with cheap wine being the best choice. It’s a good idea to start Namira’s quest as soon as you hit level five, in order to make it as easy as possible to lower your attribute.
12 Vaermina's Shrine - Requires Level 5
Vaermina's Offering: Black Soul Gem
Vaermina's Shrine is located southwest of Cheydinhal on the banks of Lake Poppad. Vaermina will want an offering of a Black Soul Gem, which can be given at any time of day or night. While there is a chance after level five that Black Soul Gems will spawn as loot on Necromancers, I've found the best way is to take a filled Grand Soul Gem to one of the four altars available to create one. The closest altar to Vaermina's Shrine is the Dark Fissure, almost directly east of the shrine, and southeast of Cheydinhal.
11 Sanguine's Shrine - Requires Level 8
Sanguine's Offering: Cyrodilic Brandy
Almost directly north of Skingrad is the Shrine of Sanguine, the Daedric Prince of debauchery. Sanguine will only speak to you after reaching level eight and offer him a bottle of Cyrodilic Brandy. There are plenty of places to find this drink, with the easiest, in my opinion, being to buy it from The Gilded Carafe or The Main Ingredient in the Imperial City's Market District. Returning with the booze will begin Sanguine’s quest, which is one of the strangest of all the Daedric quests but definitely one of the funniest.
10 Malacath's Shrine - Requires Level 10
Malacath's Offering: Troll Fat
Malacath is the Daedric Prince of Lies and Deception, and is most frequently worshiped by orcs who see him as the First Orc. Malacath's Shrine is northwest of Anvil, and almost directly west of Kvatch, tucked away in the hills. Malacath will only speak to those who are at least level 10 and bring an offering of Troll Fat to his altar. Troll Fat is very easy to get as it drops from most types of dead trolls. Trolls will spawn regularly in dungeons, with caves and mines being the best options.
9 Meridia's Shrine - Requires Level 10
Meridia's Offering: Bonemeal, Mort Flesh, Or Ectoplasm
A short walk to the west of Skingrad's stables is the shrine to Meridia, Daedric Prince of Life and Light. Often seen as one of the 'good' Daedra, Meridia hates anything undead and requires an ingredient from an undead creature as an offering. Good examples of these are bonemeal from skeletons, ectoplasm from ghosts, or mort flesh from zombies, which is the easiest to get as a zombie is encountered in the introductory escape from the sewers. Bringing any of these to Meridia after level 10 will begin her side quest.
8 Nocturnal's Shrine - Requires Level 10
No Offering Is Needed For Nocturnal
Nocturnal’s Shrine is located northeast of Leyawiin, just off the road. Nocturnal is the Daedric Prince of Night and Darkness, and operates as the patron god of thieves, with her playing a huge role in Skyrim's Thieves Guild questline.

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In Oblivion, Nocturnal does not require any offering to begin her quest, with the only prerequisite being that you must be level 10 or higher. This is a great quest that rewards the Skeleton Key, an unbreakable lockpick, and should be a must for any thieving playthroughs.
7 Peryite's Shrine - Requires Level 10
No Offering Is Needed For Peryite
Peryite's Shrine is located almost directly east of Bravil, on the banks of the Silverfish River. Just like Nocturnal, no offering is needed for Peryite, and the quest will begin as soon as the shrine is interacted with.
Before level 10, Peryite's followers will not be asleep and instead will be standing silently in a circle.
Peryite will explain that his followers’ souls have become trapped in Oblivion and must be freed. Peryite's is one of the simpler Daedric quests, as he will teleport you directly to the area in Oblivion where his followers are trapped. After this very straightforward dungeon crawl, you will be rewarded with the excellent Spell Breaker shield.
6 Mephala's Shrine - Requires Level 15
Mephala's Offering: Nightshade
Mephala had one of the more notorious Daedric quests in Skyrim, and those who want to see what she has in store in Oblivion can find her shrine north of the Imperial City, just a short walk from the Roxey Inn. Mephala will want an offering of nightshade after level 15, which must be placed on the shrine between midnight and five in the morning. Nightshade can be found easily along the south of the map between Kvatch and Bravil, or purchased from The Main Ingredient in the Imperial City’s Market District.