Doug,

First get the water tested. Salty taste and slimy feel sound like soft
water, but sticky and bad tea sound like really hard water. There is not a
lot you can do to tune up an ion exchange water softener.
If the unit has not been disassembled and cleaned in a few years it may
be time for a service call. If you have the manual and a source for parts
this is DIY. I think that the resin lasts about 15 years so if it's old it
may be time for replacement.

Dave M.