The conventional way to say this would be, "I don't like bread, rice, or porridge."
"Neither/nor" is normally used only when there are two things under discussion, and when we are contrasting them. Like, "He wanted to neither sit nor stand." It's awkward when there are more than two things, and not generally use when they are in the same "category".
Also, you shouldn't say "I don't like neither ..." This is a double negative and redundant. You can say "I like neither X nor Y" or "I don't like either X or Y".
What's wrong with simply, "I don't like ..."? If you're trying to sound less negative, to make it a weaker negative, then as Phil suggests, you could add a qualifying word, like "I don't particularly like ..." or "I don't really like ..." But note a curious English idiom here: "I don't really like X" means I dislike it a small amount. "I really don't like X" means I dislike it a lot.
- Very Late Addition in response to a comment *
RE '"I don't like bread, rice, or porridge". Isn't the meaning of it that I don't like at least one of them but not necessarily all of them?'
In a computer program or a mathematical theorem, it might mean that. But not in ordinary English. Yes, in boolean logic "if A or B" is true when A is true or B is true. But that's now how it works in plain English. Occasionally someone in a field that works with boolean logic will make a joke like this. Someone asks, "Are you coming on Tuesday or Wednesday?" and they say "Yes" and smile smugly, meaning that it is true that they are coming on Tuesday, or it is true that they are coming on Wednesday. What the person asking the question means, of course, is on which of the two days are you coming. A responsive answer would be "I am coming on Tuesday", or "I am coming on Wednesday", not "Yes" if you are coming on one of those days and "no" if you are not. (The fact that programmers and mathematicians think this kind of joke is hysterically funny probably says something about us, but that's another story.)
In ordinary English, if you say, "I don't like bread, rice, or porridge", you mean that you don't like any of the three.
If someone is asking a question, "Do you like bread, rice, or porridge?", it can be ambiguous. It can mean, "which of the three do you like?" or it can mean "do you like any of the three?". If the waiter asks, "Would you like soup or salad?", he probably means "which of the two".