Some reasons why the Joads buried Grandpa themselves
In addition to the excellent answers by simoncat, there is the simple fact that the Joads couldn't afford to pay an undertaker or to buy a cemetery plot for Grandpa. They were probably accustomed to burying their own dead on their own land, and it came naturally to them to do the burying themselves, even though they no longer had land of their own.
There are a few reasons here. One is that the Joads have to keep moving. They need to get to California or they will simply starve. Also, being cramped in the back of an old jalopy with a corpse isn't very healthy. The Joads are fiercely loyal to each other and would never let him be buried by strangers. Grandpa Joad loved the land and didn't want to leave. The Joads make sure he is buried in an appropriate spot. Casey was a preacher so he was there to give old Grandpa a simple elegy.