1. I had better listen to your advice.

2. I would rather listen to your advice.
3. I had better stay at home than go out.
4. I would rather stay at home than go out.
(Which ones are right? Can we use all the expressions?)

All are correct, and all are used. =)

1 and 3 mean it would be a bad choice not to do the action of the verb.

2 and 4 mean "I prefer..."

1 and 3 are advisable to do.

2 and 4 are your preference.

All of the expressions you listed are grammatically correct and commonly used in English. However, there are subtle differences in meaning between them.

1. "I had better listen to your advice." This expression suggests a stronger obligation or necessity to listen to the advice. It implies that it would be advantageous or the preferred course of action.

2. "I would rather listen to your advice." This expression indicates a personal preference to listen to the advice. It suggests that listening to the advice is more desirable to the speaker, but it may not carry the same sense of urgency or obligation as "had better."

3. "I had better stay at home than go out." This expression implies that staying at home is the more advisable or safer option compared to going out. It suggests that going out may have negative consequences, so staying home is the better choice.

4. "I would rather stay at home than go out." This expression communicates a personal preference to stay at home rather than go out. It indicates that the speaker finds staying at home more enjoyable or preferable in some way.

In summary, while all the expressions are grammatically correct, they convey slightly different nuances in meaning. The choice of expression depends on the specific context and the intended meaning you want to convey.