These are some very interesting sentences. Could, would, and should can be very similar and can often be swapped. However, there can be subtleties that change depending on which is used.
If it should rain tomorrow, the party would not be held.
Means: "If it rains tomorrow, the party will not be held." Should here is rather generic, and just used to start the conditional statement. Would describes the result of what happens if the condition does occur.
If it could rain tomorrow, the party should not be held.
Means: "I think it is a bad idea to have a party if it might rain tomorrow." This time should is the result and does describe the speaker's opinion. Could is the start of the conditional, but is different than "If it should rain..." because this time it implies that the result is the same whether it does rain or if there is simply a possibility it might rain.
If it would rain tomorrow, the party could not be held.
Means: "If it rains tomorrow, then it is impossible to hold the party". In this case "would" is also a generic start to the conditional statement. Then "could not" implies that the result is impossible ("the party could be held" would mean there is a possibility of holding the party, "could not" is a very strong negation which means there is "no" possibility).
These examples all show some of the different subtleties of each word (and it's location in the start/result of the conditional clause).
The second, longer example is mostly different from the above. It is less about conditionals, and more about the speaker's opinions.
They should have to work to pay for the education they would have had for free, and even then they should be put in a special school with marine drill sergeants keeping them in line.
This is rather tricky because it has nested clauses. Trimmed down, it says "They should pay for X and they should be under strict discipline." In this case "ought to" is a good replacement for the word "should", though I am not sure if the dictionary translation for that would be any different. The speaker believes that if the world would be perfect, then "They do pay for X, and they are under strict discipline" would be true. Now, on to X, "the education they would have had for free". The phrase "would have had" implies that there was some conditional that now is negated.
I think the speaker here is talking about education in prisons. It would be more clear to say "They get a free education now, but I think they should pay. I also think it should be very strict."