Here goes...
When the washing machine discharges water, I get a strong sewer smell from the kitchen sink.

1. Washing machine is located in the basement and empties into a utility sink.
2. Both kitchen sink drain and utility sink drain enter into the same cast iron pipe located in the concrete floor (utility drain enters cast iron pipe about one foot the left of the kitchen sink drain. The cast iron pipe continues beneath the floor to the right).
3. When the washing machine drains, I get gurgling and some splashing in the kitchen sink.
4. House was built in 1920's.
5. Vent pipe is REALLY high! (Three story house and I'm afraid of heights!)

Do I have a blocked vent problem?

Thanks for you help.

It doesn't sound like a vent problem. Sounds more like you have a partial blockage downstream from the washer. It might be possible to snake the line out from the washer stand pipe. You will hit a return bend in the trap about 3 feet in but once you're past that it's a clear shot, Good luck. Tom