You want the Arduino to be able to read 16 voltages from 0 to 5V?
A multiplexer with 16 inputs, 4 select lines, 1 output going into an analog input pin could do that.http://www.digikey.com/product-detail/en/74HC4067N,652/568-7817-5-ND/1230423http://www.digikey.com/product-detail/en/DG406DJZ/DG406DJZ-ND/821393
I don't know if the switch resistance will impact the signals you want to measure.
Parts with lower switch resistance are available, will need more control lines to select a channel thohttp://www.digikey.com/product-detail/en/ISL8499IVZ/ISL8499IVZ-ND/1034830
and they're all surface mount. All the thruhole parts are in the 80-100+ ohm range.
Or two 8-channel ADC chips with SPI interfacehttp://www.digikey.com/product-detail/en/MCP3208-CI%2FP/MCP3208-CI%2FP-ND/305928
12-bit data for better resolution, and also a faster conversion rate than the '328P internal ADC - 100K vs 9-10K.