Circuit Breakers on and outlets not working
Lost a Neutral
Initially, this sounded like you lost either one of the hot legs or neutral. Both are serious, though in slightly different ways.
But based on &quot;odd and even breakers&quot;, I think we can all agree this is a classic Lost Neutral.
What kind of a tester are you using? Based on &quot;only one light&quot;, it sounds like you are using something like:

Originally I was wondering &quot;which light&quot;. But as Harper pointed out, if it were a lost leg then the outlets on that leg would show no lights so one light would also indicate lost neutral.
If you lost your neutral then everything will work in strange ways. Some things (e.g., LED lights that can accept a broad voltage range) may work fine. Other things may work slowly or not at all. Other things might get overvoltage and have more serious problems - e.g., light bulbs burn out, electronics &quot;fry&quot;.
A lost neutral can be very dangerous.
However, in most cases, a lost leg or a lost neutral is a power company problem - and the power company will fix it. If you have had any recent electrical work done in your house then call back whoever did it. If not, call the power company ASAP and tell them you think you have a lost leg or a lost neutral.