Sounds like you have root issues if the plant base seems to be rotting. Have you repotted it? If not, then it is time to repot.
Go to your home improvement store and get an orchid bark mix. Once you have the bark, un-pot your oncidium. To do this, soak the pot and medium in water for about 10 minutes, gently remove all the old medium from around the roots.
Next, using a clean knife or blade, remove the dead or mushy roots and pseudo-bulbs. Once you have the plant cleaned up, set it aside and wash the pot you plan to put the orchid into.
If your orchid pot doesn't have drain holes, you will need to either drill/burn some into the pot or get a pot that does have good drainage. Make sure the pot you choose is not more that two inchs larger around than your plant. (Don't over pot the orchid)
Place some styrofoam peanuts (non-biodegradable) or you could use some clean lava rock or styro-foam pieces into the bottom of the orchid pot leaving air pockets. This will allow for good air and drainage.
Soak the new orchid bark mix to remove the 'mud' materials from it. Using the floating bark and pieces, pot up your orchid cleaned orchid.
If you are unsure about anything, post your questions. Also, if you would like more feedback, post a photo of the plant so that we can take a look and give you advice based on what we can see. The members here grow lots of different orchids and will offer great help.
Check out these posts on Repotting Orchids
Check out this information on growing Oncidium, & Intergeneric orchids:
Oncidium Growers Information
Light Requirements:
1500 - 2000 footcandles
A bright kitchen window with no direct sun is perfect for these medium-light loving lants.
Temperature:
70 - 90 degrees F. daytime, 60 - 65 degrees F. night.
Humidity:
40 - 65 % relative humidity is ideal.
Notes:
In general, Oncidiums and the intergeneric hybrids produced with them form sprays sometimes over four feet long of tiny, often yellow or pink-tinted flowers that can make quite a show. Almost all are fragrant. They grow quickly, and it is not unusual for new pseudobulbs to stair-step their way out of a pot, throwing thin roots everywhere. These can be misted with fertilizer solution diluted from 1/3 to 1/2 strength each time the pot is watered. Oncidiinae appreciate good air movement. Plants that receive sufficient light to flower often exhibit scores of tiny brown spots on the leaves and their leaf-tips frequently turn yellow. The leaves themselves can be quite brittle and will split naturally during normal growth, so the foliage is usually not considered particularly attractive. Equitant oncidiums can be difficult, as they require a cool spell at the end of the growing season to initiate the next years flowering.
Welcome to OrchidTalk!
Cheers,
BD 