A few pronunciations!

Some of these are just sounded out and others use IPA. 
YeeHaw!


Paducah
P AH d oo k ah 

P	AH	d	oo	k	ah
pet	car	do	food	key	car

Cape Girardeau
\jə-ˈrär-(ˌ)dō, jə-ˈrä-də\
This is an audio clip so you can hear how it's said
http://www.merriam-webster.com/dictionary/cape%20girardeau


Mexia
/məˈheɪ.ə


Oceala

I couldn't find anything on this girl's name. Maybe the playwright made it up? My guess would be that the beginning  part is like Ocean. Then just cut off the 'n' and add a 'la'

Rastus 

rass tuss

is a pejorative term traditionally associated with African Americans in the US. It is considered highly offensive