Police must read you Miranda Rights and obtain a waiver if they intend to question you while in police custody and if they intend on using those statements against you. They don't necessarily have to read you Mirand Rights after every arrest (only if they want to interrogate you or ask you questions).
If Mirand warnings are triggered (i.e. police custodial interrogation) then police must advise you of your Miranda Rights and seek a knowing, voluntarily, and intelligently made waiver of those rights. If not, then you should be able to get the statements supressed and request a "Walker hearing" to determine if the statements can be used against you nor not.
Without knowing a lot more of the facts of your case, there is no way I or anyone else could determine if they should have read you your Mirand Rights or if the statements should be supressed or not. More information is needed.
If you would like, I would be happy to discuss your case in greater detail. I can be reached at (517) 614-1983.
They can use any statements you made voluntarily. They have to read you your Miranda rights before trying to elicit any incriminating information from you. However, if you incriminate yourself voluntarily, they are free to use it regardless of whether Miranda was read to you or not.
Miranda rights only apply to a person in custody. That means a person who was not free to leave. If a person walks into a police station and confesses a crime, that statement could be used even if Miranda warnings were not given so long as the person was always free to leave. Another example is if a detective comes to a person's house and asks to be invited into the house. There is no obligation for the police to give Miranda warnings in that case before speaking with the person. An exception would be if upon entering the house, the police saw contraband and decided to arrest the person in which case the person would no longer have been free to leave or ask the police to leave.
THESE COMMENTS ARE NOT LEGAL ADVICE. They are provided for informational purposes only. Actual legal advice can only be provided after consultation by an attorney licensed in your jurisdiction. Answering this question does not create an attorney-client relationship or otherwise require further consultation.