For purposes of Obosh, Urza's Rage always has a mana value of 3 regardless of what was spent to cast that spell, since that's how much mana is in the spell's mana cost (C.R. 202.3). Thus, whether Urza's Rage was kicked or not, it will deal double the damage if you control both it and Obosh, since that spell's mana value is odd (C.R. 109.5).
A spell's mana value is determined regardless of what was spent to cast the spell (C.R. 202.3). The only thing that can change a spell's mana value is the value of X chosen for the spell, and then only if the spell has X in its mana cost (C.R. 202.3e), which Urza's Rage doesn't have. See also this thread and this thread.
EDIT (May 3): Edit to conform to rule update with Strixhaven.
So if I cast Comet Storm as long as the CMC is odd on the stack RR + X (of lets say 5) Obosh, the Preypiercer ability works. It will not see the multi kicker.
So if I cast Comet Storm as long as the CMC is odd on the stack RR + X (of lets say 5) Obosh, the Preypiercer ability works. It will not see the multi kicker.
Correct. X+2 needs to be odd (as that's the CMC); kicker, multikicker and other additional costs don't count towards CMC.
In the case of Comet Storm, Obosh will treat Comet Storm as a "source ... with an odd mana value" as long as an odd value for X, such as 5, is chosen (since then Comet Storm's mana value would be odd), but not otherwise (C.R. 202.3, especially C.R. 202.3e). It doesn't matter what you pay to cast Comet Storm.
EDIT (Sep. 27): Edit to conform to rule update with Strixhaven.
The Question is
Urza's Rage 2R with Kicker (does the stack see the kicker cost)+ Obosh, the Preypiercer ability = does it do 10 Damage or 20 Damage
A spell's mana value is determined regardless of what was spent to cast the spell (C.R. 202.3). The only thing that can change a spell's mana value is the value of X chosen for the spell, and then only if the spell has X in its mana cost (C.R. 202.3e), which Urza's Rage doesn't have. See also this thread and this thread.
EDIT (May 3): Edit to conform to rule update with Strixhaven.
Correct. X+2 needs to be odd (as that's the CMC); kicker, multikicker and other additional costs don't count towards CMC.
EDIT (Sep. 27): Edit to conform to rule update with Strixhaven.