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.
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.