I have some difficulty understanding what you are saying. Do you have an ungrounded 240 V system with delta connection? And now you measure those voltages from the phases to ground?
It doesn't seem to be a problem to me. No severe unbalance - you have to expect anything between almost zero and full line/line voltage in such a system.
Is your question how to ground it? If that is the case then you obviously cannot ground the transformer center point to get a 240/138 V system. But - if your country's code permits - you can ground one of the phases and get a grounded delta with 0, 240, 240 V from line to ground. It is being done in the US and it really doesn't change much. Only that a ground fault in one of the hot phases will trip the corresponding fuse, which could be good.
I think that more and clearer information is needed before anyone can give advice here.