my 2009 iMac has no audio-input or output--no sound

They should be built-in. Note, the audio built-in to the Mac includes mini-Toslink 5.1 DTS speaker ports which support 1/8th RCA audio as well. If you have just RCA audio speakers plugged into the port, no secondary audio is possible for output. The Mac is old enough the PRAM (also known as Clock, or CMOS) battery may be running low, and need replacing. If it is less than 4 years old (the battery), then you can reset the PRAM. Lastly, check the Audio Midi Setup application in the Applications -> Utilities. This may explain why the audio input and output are improperly setup. Anything higher than 48 Hz on stereo in/out will be silent.