Ability Score Increase. Your Dexterity score increases by 2.

This isn't bad, most races get a 2+ and 1+

Size. Ratmen stand between 3 and 4 feet tall and average around 90 pounds. Your size is Medium.

You should make this a small creature. Dwarfs stand 4'4 and are medium. You are shorter than that.

Speed. Your base walking speed is 30 feet. 

This is fine, many races have that speed.

Darkvision. You have superior vision in dark and dim conditions. You can see in dim light within 60 feet of you as if it were bright light, and in darkness as if it were dim light. You can’t discern color in darkness, only shades of gray.

Again, dark vision isn't uncommon. 

Disease Resilience. You have advantage on saving throws against poison, you have resistance against poison damage and you are immune to disease.

So your immune to disease and resist poison?  That is slightly overpowered. But I'll let is pass.

Infected bite. Due to your life in the city's sewers, you have been infected by a number of horrendous diseases that have effected your physiology. You have a bite attack that deals 1d4 piercing damage forcing the creature make a Constitution saving throw against a DC of 8 + your Constitution modifier + the amount of piercing damage taken during the initial bite, on a failure the creature takes poison damage equal to your Constitution modifier and cannot be effected by any healing effects, on a success the take half damage and no addition effects. At the beginning of your next turn, if the creature failed there previous save, the creature makes another Constitution saving throw, on a success the effect is removed on a failure the effect remains for an additional round, if the creature fails three times the effect lasts until the creatures next short or long rest (creatures immune to the poisoned condition are also immune to this effect, but still take the poison damage, creatures immune to disease take nothing but the piercing damage).

This is very wordy, and I don't think that any other ( official ) race has this. I think it should be removed.

Keen Smell. The Ratman has advantage on Wisdom (Perception) checks that rely on smell. 

This to is fine, some races have something similar to this.

Natural Claws. Because of your claws, you have a climbing speed of 20 feet. In addition, your claws are natural weapons, which you can use to make unarmed strikes. If you hit with them, you deal slashing damage equal to 1d4 + your Strength or Dexterity modifier (your choice), instead of the bludgeoning damage normal for an unarmed strike.

Again, other races have this, it's not as common darkvision but...

Rodent Nimbleness. You can move through the space of any creature that is of a size larger than yours.

If you took my advice about making it small creature than you could move through the spaces of medium creatures. Slightly overpowered.

Languages You can speak, read and write Common and Undercommon.

Two fixed languages is fine. 

My analysis: Balanced, but a few features need changed.