With chlorinated city water the smell of chlorine is sometimes detectable. Some municipalities are going to the use of chloramines for sanitation and the use of chlorimines can increase the "chlorine" odor. You should be able to get a detailed analysis of your water from your water supplier--they are required to test reqularly and the results are public information. Many municipalities post the results on a web site.
In any event the chlorine odor is not an issue related to your softener.
Chlorination removes iron from water by chemical conversion and precipitation so I expect the municipality test results will show no iron or only negligable amounts of iron.
I suspect you have sediment in your water and over time the softener bed has been contaminated with the sediment. Have you confirmed that the softener is regenerating normally and that there are no obstructions in the drain line that would prevent full flow for the backwash cycle (the cycle that would normally flush out any trapped sediment)?
Do your neighbors have similar problems?
What is the material of your water pipes--plastic/copper/galvanized, etc?
Post your softener cycle settings along with the amount of resin (cubic feet or softener capacity in grains) and your city water test results.