Is it viable getting two-three Rods Of Ages provided that game will run long enough for them to max their potential? Banshees and Rylai's both look very tempting, but I rarely am unable to catch/escape someone and Force of Nature and reworked ulti grants me enough cc resistance for Banshee's passive to be all that important. Or is it a risky investment?

Resistances > health.
Health is important don't get me wrong but honestly after one RoA singed really doesn't need any more health.

Hello shutupalready

When I play singed I go:
Dorans shield, Merc threads, Catalyst the..., Sunfirecape, Banshees/Roa, rylai, force of nature
The reason for this isthat with the latest patch they made Singed a way better main tank than off tank/aoe ap dealer. which was what he was exceptionally good at before.
Sunfire makes you even more of a dreadnaught in their midst

I don't play Singed so frequently anymore but when i do:
Manacrystal, Merc Threads, Catalyst, Force of Nature or Sunfire cape (depending on enymy team), whatever i didn't get earlier, RoA, Rylai.
[If the opposing team is heavy spellcasters, consider switching Rylai/Sfc/FoN for Banshees Veil]

Now go have a good time flinging enemies