I commute daily on a road bike with Shimano Tiagra STI shifter/brake levers. The rubber hoods are pretty grimy and getting sticky, torn up and unpleasant these days. Repair and replacement of pretty much everything on my bike seems very straight-forward, but I can't figure out if these parts can even be replaced, much less how to do it. Ideas?
If you can't get a replacement hood, try making one yourself. Here I have stretched a section of 26 x 1.5 - 2.0 inner tube over the brake lever. The inner tube fits better if you cut off the tip of the "horn" of the aero levers. With these Shimano Exage Action BL-A351 levers you can slip the edge of the rubber under the plastic front of the lever to help hold it in place.
The lump at the bottom of the dip in the brake lever is caused by a metal tab. I'd cover that with a leftover piece of padded handlebar tape before adding the inner tube.
To avoid the seams on the surface of the rubber, try turning the inner tube inside out.
before you do anything, you should check the components documentation on shimano's web site, all the instructions are there - the hoods are quite widely available on order from bike shops although they don't seem to justify the $$ tag. if it's only sticky, just clean it with a damp cloth or with 1 drop of dish washing liquid if it hasn't been properly cleaned before. i use mine for over 5yrs+ its very scratched now but still don't need to replace.
I think the first thing you should do is take the hoods off the bars. Usually there is a screw or an allen key that will loosen the hood on the bar. On my hoods this is only viable when the break leaver is pulled down. After you loosen this screw you should be able to slide the hoods along and off the bar. (You might need to remove the tape).