In general, one cannot kasher china, as it is assumed to belong to the category of kli cheres (earthenware). The gemara‎{&&1}‎ states that the Torah testifies that one cannot remove from a kli cheres all that it has absorbed.
However, when there is a confluence of 1) a variety of mitigating circumstances and 2) a significant need, one can permit a special system of kashering of such utensils. Regarding a full set of china, we can assume that not being able to use part of the set would be considered a hefsed merubeh (a great loss) for most people. We are also assuming that most use of the utensils was as a kli sheini (i.e., the hot food was removed from the pot that was on a flame before it made contact with the dishes.)
The following system can be used in such a case. The dishes must not be used for twelve months so that the absorbed matter can dry out.‎{&&2}‎ One fills a large pot with water so that it preferably contains sixty times the volume of the dishes that will be in the pot at one time. The water should be brought to a boil and kept boiling. The dishes must be cleaned of all residues before the kashering process can begin. Each dish from the set should be placed in the pot for a few seconds so that the water covers it and then is removed and rinsed. The process should be repeated three times, a system which works, according to a minority view, even under normal circumstances for a kli cheres. Some say that the water should be switched before each repetition of the process.
This discussion is a synopsis taken from BeMareh HaBazak.‎{&&3}‎ One can find there additional sources and reasoning for our specific issue and should study the laws of kashering in greater depth.