A complete thread of all the Saiyan transformations in the DBS Manga in mostly chronological order.
Super Saiyan God: Far weaker than Anime SSJG, but still a league beyond SSJ3. Its only about Base x1,000~. While Goku doesn’t get a power boost from it, he can use it at will later on, as does Vegeta for unknown reasons. It has no defined stamina/time limit, or special abilities.
(Initial) Super Saiyan Blue: Identical to SSGSS in the RoF movie. It has a simple SSJ-like aura and there’s no noteworthy stamina drain. This version of Blue is shown in the early U6 Arc, but is suddenly replaced with Advanced Blue afterwards. —
— It’s likely that Toyotaro wanted to alter Blue’s rules, so he replaced this variation with SSJ God. Interestingly, this makes another appearance in the ToP Arc during Frieza’s RoF flashback, so it’s not retconned out of the manga.
(Advanced) Super Saiyan Blue: Not at all distinguished from Initial Blue narratively, but Goku and Vegeta use only this variation from the U6 Tournament onwards. The aura has distinct blobs of fire or ki in it. It is a highly taxing form: both transforming into it repeatedly, —
— and using it for too long will dry out the user’s stamina *and* power. Vegeta works around this by switching from God to Blue repeatedly, implying that only SSJG lets him avoid the transformation drain (maybe because of the god ki, but it’s never stated).
Full-Power SSJ2: While fighting Dabura, Trunks unlocks SSJ2. Later, he learns to power it up far beyond its limits. This is equal to SSJ3 in power and speed, and has no notable stamina drawbacks.
Completed Blue: By compressing his aura into his body, Goku is able to prevent his ki from leaking out, reducing his stamina and power drain to null. At first, he struggles to use this properly against Merged Zamasu, and risks blowing up his body from the pressure. —
— In the ToP Arc onwards, however, Goku and Vegeta use this form casually with no apparent drawbacks. Blue’s aura can also be channeled into attacks to power them up, which is how Goku mimics the Hakai.

Gogeta also uses this form.
Berserk: Kale starts with a noticeably taller but slim build, and gets more muscular as her ki rises indefinitely. Assuming SSJ Caulifla = Base Frieza and Kale ~= Caulifla, then Berserk (peak) = 250,000x. The drawback is that she would explode if left to power up endlessly.
Kale's power stabilizes when Caulifla fuses with her into Kefla. This form is either known as Mastered Berserk Kefla, or just SSJ Kefla. Since Kale is far beyond Caulifla, Kefla is equal in power to Kale, like other power-gap fusions, but being sane lets her fight effectively.
Power-Stressed Blue: Goku magnifies his ki in Completed Blue as far as he can go at the risk of destroying his body. A Kaioken-like aura covers him. This powers him up noticeably. Whether this is *just* Blue Kaioken or not will be one of the timeless debates of the DB fandom.
Blue Evolution: This form is identical to its anime counterpart in its purpose, but the opposite in everything else. Vegeta unlocks it during a furious outburst, pushing Completed Blue to a new level. He’s able to get some hits on Jiren, but nothing significant.
Jiren confirms this form has more raw power than Omen. The aura is similar to Advanced Blue’s, with its signature blobs forming a second layer to the aura, strongly resembling Anime SSJB. Its stamina drain is implied to be slightly more than Completed Blue, which isn't much.
Ultra Instinct Omen: Manga Omen emphasizes deflecting attacks from vital points, minimizing damage taken. Goku learns to use this "at will" in the ToP, but temporarily. He learns it permanently with Merus in the Moro Arc. However, it still drains his stamina quickly. —
— Goku can also hone this form to different extents, using it at a restrained level or at full power. This form is always slim like SSJG, and has a simple aura surrounding it. In the manga, Omen explicitly uses god ki.
Power-Stressed UI Omen: Out of desperation, Goku magnifies Omen’s power beyond its abilities. He regains his muscular physique and powers up, but loses most of Omen’s key advantage. The aura strongly resembles Advanced Blue’s. This form lasts an extremely short length of time.
Completed UI: After honing UI Omen, Goku briefly taps into its 'final' variation. Because he unlocks it prematurely in the ToP, it is very inefficient and drains all his stamina quickly, but it put him on the level of Jiren and Beerus. —
— He learns to hone it fully in the Moro Arc, and can use it at will permanently with no significant stamina drain. Like Completed Blue, this form has no aura. In the ToP, Goku’s body is slim like SSJG. In the Moro Arc, it is distinctly muscular like Power-Stressed Omen. —
— When Goku is low on power, he loses the ability to control this form, and needs to heal or be recharged with extra god power.
Multipliers (estimates):
God: 1,000x
Initial Blue: 1,200x (<< Advanced Blue)
Advanced Blue: 2,000x
Completed Blue: 5,000x
Power-Stressed Blue: 10,000x
UI Omen (full power): 20,000x
Blue Evolution: 25,000x
Power-Stressed Omen: 50,000x
Completed UI: 1,000,000x
Explanation:
In the U6 Tournament, SSJ Goku was in the same ballpark as Advanced Blue Vegeta at 10% of his power. A bit of wiggle room puts God and Blue in the early 1k's. Completed Blue should be stronger than 2 Blues (based on the Black Arc interview with Toyo).
Unlike in the anime, Omen isn’t leagues beyond Blue. The huge gap between CUI and everything else is because it’s equal to Beerus/Jiren in the ToP, as well as Vegetto Blue. That means CUI = Advanced Blue x400~, but I rounded it up to x500 because 1,000,000 looks better.

Numbers.
I have been alerted that I cannot read, and Jiren actually said that Omen is stronger than Blue Evolution. In that case, I'll just flip their multipliers around and call it a day.

I liked thinking that Goku was only stronger in Completed UI, though 😕.
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