In Into the Odd an unarmoured man with a simple weapon causes 1d6 damage and subtracts 0 from incoming damage (Armour 0). Below is a handy reference guide for what it means to go above this.
To get +1 to Damage and Armour be mounted or large. Otherwise, get of a Martial Weapon, something purpose-made for extensive combat use like a longsword or bow, or a more simple two-handed weapon like a big club, and light armour or a shield. When fighting in a unit, outnumber your opponents by less than 2-to-1.
To get +2 to Damage and Armour be the size of a rhino. Otherwise, get a two handed martial weapon like a halberd, or an exceptional crossbow or gun, and light armour with a shield or a suit of full armour. When fighting in a unit, outnumber your opponents 2-to-1.
To get +3 to Damage and Armour be the size of an elephant. Otherwise, find the most expertly made two-handed weapons in the world and get full armour with a shield. When fighting in a unit, outnumber your opponents 3-to-1.
To get +4 to Damage and Armour you'd better be REALLY big or outnumber your opponents 4-to-1.
Example of Use
I want to make a huge land-eel with a horned crocodile-head to chow down on intruders.
I figure its horns are equivalent to a Martial Weapon (+1 damage) and it's roughly as hefty as a rhino (+2). This gives it an attack of 1d6+3 damage. If I was feeling generous I'd raise this to 2d6.
As mentioned, it's around the mass of a rhino (Armour 2) but lacks any real toughness to its hide, giving it an Armour of 2. Throw together its Ability Scores based on the range of 0-20, with 10 being the average human and decide whether it's important enough to get just 1d6HP or the typical cap of 5d6.
HORNED EEL-IGATOR
STR 15, DEX 8, WIL 6, 7HP, Armour 2.
Attacks for 1d6+3 Damage. Surprisingly cowardly if faced with a ferocious opponent. Quite content to snack on plants if it weren't for it being deliberately starved into aggression.
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