This sounds like a very technical question. Could you give us an example, or at least tell us where you found these expressions?

It sounds like technical language, either from mathematical logic, or from Boolean algebra used in designing digital circuits. For example, if you have a AND gate with two inputs, A and B, and an output C, the truth condition for C is that C has the value "true" if A and B both have the value "true."

It's not clear what you are asking. If I was to take a guess then I would say that a truth condition is the part of your sentence which describes what is required for the sentence to be true, while truth value are what needs to be compared. For example "All roses are blue". Here the truth condition is that Every flowers of a certain type must be equal to a certain colour and the truth value would be roses and blue. The above example would be false, however if we replace the truth value of blue with red, then the same truth condition would be true. (all roses are naturally red, lets ignore blue roses that have been dyed or genetically modified) Another example could be "My name is Bob". This one is simple because for the sentence to be true (the truth condition), the name I gave above must match my actual name. The truth value here would be the name "Bob", because that is what you need to look at to see if my name is actually Bob. As you can see this is not true because Caleb and Bob are not equal. Again, This is just a guess as the question is a bit vague but I hope it helps.