There is a few things here. There is both picking the right champion, and knowing how to manage the wave so that Nasus gets as little free time as possible.
Vayne is a VERY bad choice for vs nasus. I have used Nasus vs Vayne and built pretty much just armor and no health and brutally messed her up even tower diving. She
Ive found Trundle to be quite effective, Teemo when going Grasp and more of an on hit tanky build... anyone who has some sort of usage outside of auto attacks will be able to do something.
Mordekaiser with Hail of Blades will also do quite well if you are good enough with him, the Nasus will expect to have the auto attack advantage on you then you just pop out having Hail of Blades going on your Q and shield up most of his damage. Might or might not be able to kill him, but you can set him back and you can eventually poke him down and potentially kill him with ultimate later on (i recommend liandries, thornmail, and tabi vs Nasus if you are on par with him.... rylais before thorn if you are ahead).