What do you want to know?
It sounds like you have all the information you need. If what you say is true, then they should be "Basra" pearls- which is a shorthand way to say the pearls are from the Persian Gulf.
Because they are mostly button pearls, they are not as valuable as round pearls, and they do look like freshwater pearls to many, so I suggest you go to a local, respected pearl dealer and discuss getting them certified as "real pearls" or whatever English phrase they use. Nobody knows more about Basra pearls than pearl dealers in India. Based on the karat weight and actual range of sizes, a local respected Indian pearl dealer can tell you their value on the current market. Also, the biggest market for Basra pearls is right there in India. Out here in the rest of the world, they would be competing with cultured freshwater button pearls from China in looks- and probably not get the respect they deserve, because of the shapes looking so freshwater.
Has your family just kept them in strands like that for 150 years and not used them for jewelry? The tassels don't look old, so they are new or have been packed away for generations, but they don't look packed either. What have they told you about them? How do you know they have been lying around unused for 150 years? Your family has so many Basra pearls, the women can't wear them all, so leave some lying around on strands?
Or were those taken apart recently and put back into unfinished strands, for sale purposes? Please tell us more.