Were there any atypical or unusual weapons?
During the Sengoku Jidai or what we call in the West, the Warring States Era the samurai had evolved from previous times. For example, it was now more common for a mounted samurai to be wielding a spear rather than the yumi which was the bow. It was pretty large and it was thought to be less effective now from horseback. This isn’t to say that archers were no longer needed, they were still in high demand, but now they were usually not on horseback.
Before I move on to the next weapon, I should explain something about the spear. There were multiple spears such as the yari which was more like a lance actually. This type of spear was used more for stabbing rather than slashing. For slashing you’d be looking more at a naginata which has a curved blade ideal for that style of attack, or you could look at a nodachi which was a long sword with a really long handle.
This brings us to the famed katana. Samurai weren’t known for shields, and the samurai sword (as it’s called) was used for both purposes. If you want to get down to the nitty gritty technicalities of each weapon like how a katana acts as a sword and shield, we can; but otherwise, the other weapons you would see the samurai carry would be either the wakizashi which is a short sword or a tanto which is a dagger. The duo between a combination of the katana and one of the latter 2 weapons I just named was known as daisho. This was the “star” the “medal” or “badge” of the samurai.
I must stress that in the Sengoku Jidai the functionality of weaponry was more important than anything. It was really a dog eat dog world in this period of Japan so the Samurai would also use the Tanegashima which is a an arquebus style firearm known as the matchlock gun. These weapons were acquired in the middle of the 16th century by powerful Daimyo or Lords such as the famous Oda Nobunaga from the Portuguese.
Takeda Shingen another powerful Daimyo of the era was quoted saying:
Decrease the number of spears, and have our most capable men carry guns. From here on out, the guns will be the most important weapon.
Warriors of Medieval Japan by Stephen Turnbull
A Military History of Japan: From the Age of the Samurai to the 21st Century by John T. Kuehn
The main weapons they used were common: spears, bows, guns, swords, knives. Spear were various, ranging from cavalry lances to long pikes to short infantry spears (perhaps about 8' long). The period saw a growth in the size of armies, with much of that growth coming from larger numbers of infantry - the old days of the Japanese battlefield being dominated by cavalry (especially mounted archers) was gone, and the bow was a common infantry weapon, accompanied by the gun after the introduction of the matchlock arquebus. Swords were often sidearms, used as backup weapons (e.g., if the spear broke, or archers or arquebusiers found themselves in close combat. Knives served as utility blades and last-ditch hand-to-hand weapons, and were also valuable if wrestling (especially when wrestling in armour, as they can be used to exploit gaps).
Polearms other than spears were used, primarily the naginata (basically a glaive - a shortish sword-like blade on a pole). This had previously been much more common, but the spear had displaced it as the main polearm.
Samurai wielding these weapons of were supplemented by a usually larger number of ashigaru, lower-status infantry.
The large number of Edo Period hidden/disguised weapons and less-than-lethal police weapons (e.g., the manrikigusari (two weights on a chain) and the jutte/jitte (a metal truncheon)) were either yet to be developed, or much less common. These were not battlefield weapons, so they don't appear in any significant numbers of the battlefield. One exception in the gunbai, a fan used by commanders for signalling to their troops on the battlefield, which were often stout and could be used as emergency weapons (more likely for parrying than striking); I briefly discussed these fans in https://old.reddit.com/r/AskHistorians/comments/cob7xf/a_common_trope_in_japanese_martial_arts_fiction/
As for atypical and unusual weapons, it depends on exactly what you might consider atypical and unusual. For example, some consider the usual Japanese bow, the yumi, unusual for it's asymmetry (the upper limb is much longer than the lower limb). Some other candidates for atypical/unusual are:
odachi/nodachi: long two-handed swords, which could be 5' to 6' long (total length).
cannons: used in sieges
pavises: large stationary shields used to protect archers and arquebusiers in sieges and field battles.
nagamaki: a long blade on a long handle, approximately half-way between a naginata and an odachi/nodachi. Uesugi Kenshin, a powerful Sengoku Jidai daimyo, was said to have a crack unit equipped with nagamaki.
jingama (camp sickle): a short-bladed sickle used to cut grass for horses. These were often more ornate than farmer's sickles (kama), and are possibly the ancestor of the kusarigama (ball-chain-sickle).
omi-yari: a spear with a very long blade (often 2' to 3' long). Hafts were usually fairly short.
kuda-yari: the tube-spear, where the lead hand grips a metal sleeve about the haft. This allow faster "pool-cue" thrusts with the spear than if it has to slide through the lead hand. This sleeve was supposed invented by Hozoin Inei (founder of the sojutsu school Hozoin-ryu) late in the Sengoku Jidai.
Spears with blades of more conventional length could have various side spikes on the blade (e.g., jumonji yari, kama yari, katakama yari) or a bar for parrying and/or trapping on the haft below the head.