Curry Leaf Plant with Disease Problems

I have a curry leaf plant for the last 8 years. It recently got a white fungus on the woody part of the plant. This has dried one half of the plant and we had to cut that half. Now it is spreading to the other half. What do I do to control this to save the plant? It also has a bug that sticks to the stem and leaves. It is very sticky and very messy.

It sounds like you have powdery or downy mildew, plus scale insects. Hold the plant upside down (put newspaper over the soil and tape it down), in soapy water and rub off as much of the mildew and scale insects as you can.
The next thing I would do is take a few cuttings of the healthy part of the plant and try to root them in sterile soil in a clean pot, enclosed in a clean zip-lock plastic bag. Make very sure that you again swish the cuttings in soapy water before potting them, since the crawling stage of the scale insects you seem to have would love to leave with the cuttings and live on them!
Lastly, spray the plant with neem oil at the rate of one teaspoon neem oil with half a teaspoon dishwash detergent or Safer's soap in one liter of water. It should help with both problems. The rotten onion smell will go away in a day.
If you can't stand the smell of neem oil, try Cinnamite instead. It is a cinnamon oil and wood (methyl) alcohol emulsion and should be srayed at the rate of one teaspoon cinnamite per litre of water.