From the look of the pseudobulbs, I think the oncidiums that you got could be Onc. Gower Ramsey (Onc. Sweet Sugar), a very popular yellow oncidium hybrid that has been mass-produced and sold virtually everywhere. This is one tough little cookie, very hard to kill and under the right conditions, it grows like weeds!!!
What you need to do is potting the pseudobulbs deep, especially the new growths (I see that your cuttings are having new growths) at least an inch or so under the medium so it can root. The new roots will come out of the new growths so the new growth must be burried under the medium (where the moisture is higher and more constant) to help them. I would not add peat to the potting medium unless you plan to keep it drier than normal. Fine barks with some perlite or small pieces of rocks is good. These orchids like to be evenly (constantly) moist BUT NEVER SOGGY. Keep the plants where it is warm for now and lot lot of diffuse light will help it grow. They also like fertilizers (applied very dilute and weekly and you can fertilize them when the growth is substantial). These orchids need some cooling in order for the pseudobulbs to mature and to bloom well. So intermediate temperatures are the best for them (aka, night temperatures in the range of 55 F in order to initiate the spike). But lot of light would do the trick as well. They can bloom with only 2 mature pseudobulbs.
So have fun with them!!!