Of course bspooner is right. The tank is an usual (obvious?) installation for homogeinizing compositional changes and getting a regular stripper operation. Otherwise, these changes may result in overstripping wasting steam, or not consistently meeting product spec.
About two feet of hydrocarbons are allowed to float on top of the sour water for odor reduction. Cone roof tanks may require nitrogen blanketing for safety and odor control.
Escaping vent gases may need to be treated to answer to local environmental regulations.
Clearly, hydrocarbons in the feed stabilization tank should be removed before emptying the tank to prevent the SWS to become an oil stripper.
The feed, pumped on flow control, is generally pre-heated by exchange with outflowing stripped water. A LP steam reboiler is usually used rather than adding water by injecting live steam, thus saving condensate while operating the stripper at lower pressures.
I believe it was mentioned in the previous link that the top of the stripper should be kept above 180 deg F, to avoid sublimation of ammonia salts, that may plug everything, including the tower's overhead piping.
A particular problem arises when treating FCC waters containing cyanides which may require titanium overhead condensers to prevent corrosion under deposits.
One of the procedures to avoid using a condenser and reduce corrosion is using a pump-around cooling system. Pump-arounds, being liquid-filled systems wouldn't permit deposition of solid salts.
Good luck.