For build 1, you really don't have a lot of tank, or damage output, for build 2 you have decent tank, but it can't offset the terrible damage output.

I understand your hesitation at the second build I figured I'd include it only due to the fact that the build has net me more than 2 penta kills. Second Rylai's early i've found to be quite useful as the extra damage output and slowing effect make netting kills much easier. As for the inability to tank turrets I tend not to need to in favor of walking under hitting with siphon then backing until the enemy is low enough they either back for ult+ignite gets me a pet.

The first build is ok, but I would get FoN before Ryalai's, otherwise you dont regen health fast enough. The weakness is not much armor until late game, so you can't towerdive well.

The second build is bad. Warmog's is a bad first item because Mord does not need HP early game, he has his shield that benefits from armor and magic resistance and not HP. If you get FoN before Warmogs then it's an ok build.

Some cool items for Mord you could try are boots of swiftness, I find they work great for kiting. Also Hextech Revolver is awesome it keeps your HP nice and high. Rabaddon's is cool but quite expensive. Mord doesn't die easily so Mejas is sometimes a cheap way to get lots of AP. Anyway just thought I'd throw some ideas out there.

As for me my first three items are normally swiftness boots, Randuin's Omen and Force of Nature.