How do you pronounce sawing and soaring?

[BroccoliSpears]

Do they sound the same?

No

Sor-ing
and
Sor-ring

iyswim

no as one has an 'r' between the syllables

but the other doesn't have a 'w' sound more a lack of consonant between the two syllables

saw - ing
rhymes with claw - ing

and
sore -ing

Saw - ing

Sore - ring

like custy

sawing is sort of "su-ing" or "soing" maybe "soying" (I can't actually write it, I'm saying it to myself and it doesn't sound like any of those, but it's the closest I can get)

soaring is "sawring"

so sawing is sort of an elongated soing (rhymes with boing)?

No. Doesn't rhyme with boing.

More like sor-ing with a silent r.

Like Custardo.

Chopping and flying