If you are using Silvaco for your plots, Silvaco employs extract command in deckbuild to extract various parameters from the plot. Demo websites released by Silvaco on google search should give you how to write your codes.
Books by Professor Dieter Schroder (a pioneer in semiconductor device characterization), Professor Yuan Taur ( a pioneer in semiconductor device physics and modeling) and Professor Juin Liou ( a pioneer in semiconductor device physics and modeling) should give you clues how to employ strong methods to extract parameters related to MOSFET even organic FETs with little margin of error. These books must be available in Amazon and other US Engineering bookstores and you can use google scholar to cite their names and see if you can get pdf copies of their books from their list of published articles. Professor Baquer Mazhari in IIT Kanpur India also does research in organic FET. You can see whether he published any book or book chapters related to device characterization of OFETs.
Off course by giving extract command in deck build using SILVACO TCAD ISE you may extract most of parameters of a device. To know extract command read Silvaco user manual in detail. You will get most of the commands there.
I found couple of excellent papers on OFET and OTFT. I have attached here couple of papers. Some of them are thesis based so more general and widespread characterization methods are described here. Couple of them are research articles and more up-to-date modern characterization methods are employed in these articles.
I hope you will find these articles useful for your research.
You have the I-V data points of a transistor in excel sheet.
Then to get the threshold voltage you need only to plot square root of ID versus VGS in the saturation region where VDS> VDSSAT. You get a straight line which can be extrapolated to ID=0 to get its interception with the VGS axis= Vth
The mobility can be extracted by plotting ID versus VDS at a given VGS> Vth in the linear region, then use the relation
ID= mu Cox W/L( VDS( VGS-Vth)), from the slope one can calculate mu, the mobility knowing Cox, W,L VGS and Vth.
In the subtheshold region you plot Log ID versus VGS in the saturation region such that VDS> VDsat and then calculate the VGS value for one decade of the drain current. This is the required gate voltage swing. For the standard I-V relations for MOSFET transistors please refer to the book:https://www.researchgate.net/publication/236003006_Electronic_Devices