I was bored so I started a list of possible units and gave them some discriptions. I'm still working on it so some things are off, most of the units are based on truth others may be more off. The Warrior monks are fleisable since they were trained in diffrent weapons and sometimes mounted.
Infantry
Axe
Ono Ashigaru
Simple Farmers, Woodsmen, Merchants and other commoners taking up arms against their enemies or even their Daimyo. In times of extreme circumstances the Daimyo may levee peasants into service to bluster their ranks, to defend their lands or in even more desperate times use them in their front lines. Often or not in times of war or rebellion the commoners use what weapons they get their hands on to over throw their oppressors, the Ono (axe) if available is favored and can inflict serious wounds even to armored men. These simple folk should not be looked upon to hold their ground for long, they have very little to no training in the art of Bushido and have little stomach for combat.
Strengths & Weakness
Axes: bonus vs Armor
Very Low morale and will rout at the first sign of danger
Battle field uses: Cheap, can be used for flanking engaged units were their axe can do damage to armored units.
Ono Warrior Monks
Warrior Monks are brave men who worship Buddha and fight with zeal unmatched by any samurai. These Warriors use the Uno or Axe to defend themselves and their temples. The Ono in the hands of an experienced warrior is a deadly weapon indeed, just as it can fail a mighty tree it can do the same with any opponent.
Strengths & Weakness
Axes: bonus vs Armor
Standard Warrior monk traits
Low defense
Battle field uses: Can fight any infantry but weak against Bow and Cavalry.
Mori Ono Sailors (Mori clan only)
These men are Hardened sea goers, the Ono or axe was a preferred weapon on ships were it could be used to cut ropes or chop Oars of the enemy ship to either repel grapples or disable the enemies ship. The sea shapes brave men and stout fighters, however they belong on the seas so fighting on land can prove difficult, still these men carry the Ono and can conflict considerable damage to armored troops.
Strengths & Weakness
Axes: bonus vs Armor
Brave
Low defense
Battle field uses: Flanking armored units.
Sword
Katana or No-Dachi Warrior Monks (Ikko-ikki, Shimazu and Uesugi)
Warrior Monks are brave men who worship Buddha and fight with zeal unmatched by any samurai. These Warriors use the No-Dachi or a Katana to defend themselves and their temples.
Strengths & Weakness
(not sure)
Battle field uses: Good against infantry but weak against Bow and Cavalry.
O-yoroi Warrior Monks (Uesugi, Ikko-ikki)
A rare slight indeed, seeing Warrior Monks cladded in heavy armor. Temples were offered much tribute, one tribute being some of the finest armors and weapons around. These men dawn the heavy armor to defend against would-be enemies to their sect or perhaps even for a bribe. They carry the Katana and Tantoshort sword into battle.
Strengths & Weakness
Armored monk what more can I say?
Very Slow
Expensive
Low unit numbers
Polearm & Spear
Oda Naginata Ashigaru (Oda Clan only)
Placing such a weapon in the hand of an Ashigaru seems like a prudent step, its such a dangerous weapon and after all strength in numbers! These men are slightly more trained then the typical folly Ashigaru, however they cost more to train and maintain.
Strengths & Weakness
Standard Naginata bonus
Little armor
Cheaper then elites but higher then standard Ashigaru.
Battle field uses: Cheaper alterative to an all round useful weapon.
Ranged
Cavalry
Takeda & Oda Mounted Ashigaru (Takeda & Oda clan perhaps Ikko-ikki )
Desperate indeed is the Daimyo to mount Ashigaru! The Horse is not for lowly Ashigaru, however their cheap to maintain and their enthusiasm for being entitled such a magnificent beast could perhaps make for good scouts, flanking and running down routed units.
Strengths & Weakness
Cheap to maintain
Not disciplined & low morale
larger numbers?
Battle field uses: Scouts, running down routed units and chasing mounted bow.
Mounted Warrior Monk Archers (Chosekbe, Takeda, Uesugi and Ikko-ikki Clans)
Mounted Warrior Monks (Takeda and Ikko-ikki Clans perhaps Uesugi )
Ships
Atakebune Tekkosen (Oda)
A large Atakebune, its superstructure may have been reinforced with iron plates against cannon and fire arrows. Oda used them against Mori's navy and defeated them. They are armed with a few cannons and numerous large-caliber arquebuses
Mori Atakebune
Similar to the above maybe?
Hero Units
pirate Kuki Yoshitaka hero (Oda)