From past experiance, I would open the hood remove the oil filler cap and look for signs of coolant in the oil it would look like a gray color with consistance of mud, also remove the oil dip stick and check for the same thing.
Then check the coolant overflow resivor and see if it has the same signs of oil in the coolant.
If the engine is at operating temp check the trans oil level and see what color it is and if it smells like burnt popcorn.
Drive the car and pay close attention to the way the engine sounds and how the tranny shifts through the gears. Im sure others will chime in.

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'85 F250 6.9L diesel 2wd XL XC LB Centurion, Gone
'95 Mercedes E 300 Diesel W124.131 with a OM606.910 and just over 200k on the clock, needs top end engine work and a transmission.
2000 S500 W220 with a 5.0L V8 gas power.