Thanks BSOS for this:

This works 75% of the time:
even better if they wall off

15 pool
14 extractor (3 on gas)
16 overlord
16 queen

first 100 gas spend on ling speed
next 50 gas spend on baneling nest
then just pump lings till you have about 200 gas and tech

when you have about 20-24 lings, push out, and in his natural morph about 6 banelings

send the banelings in first to break down the supply depot wall and run in with lings
sometimes i make a few extra banelings and send them after the harvesters while my zerglings attack the MM; or you could use the banelings on the marines (its super effective!)

after first push, get more lings and tech to muta, expand
slowly tech to broodlord

just use bane/ling/muta to keep him on 1 base for as long as possible
finish him off with broodlords

or instead of broodlords get infestors, they always help since they can 1 shot a group of unupgraded marines

Additionally, warnipple states:

The only way Zerg beat Terran in 1v1 is with an economical victory.

Expand early because Terran can’t really do anything about it and get Banelings + burrow. Banelings easily kill Marines and its even better when they can be hidden in a choke point (they can explode while burrowed).

As for marauders. Once the marines are dead you can just use air units to kill them.