Can I teach English without a degree in Indonesia??

As it stands today, to qualify to teach in Indonesia you need a degree (any as long as you have transcipts), and at least 1 years teaching after graduating, a teaching certificate, and a medical check from a hospital in Indonesia.  Also over 25 and below 50.

However, dependent on your skills you can find work in many schools in Jakarta and may be other cities if they feel you are suitable for them and they will arrange the necessary paperwork for you.

Should you get a wife sponsored visa (spousal visa) this does not allow you to work but stay in the country up to 2 years but it does allow you to provide for your family. If you get a business visa you need a sponsor and also understand that you can work only as the visa states and at the place named. If you get a school sponsored working visa (KITAS) then this allows you to work here legally for the duration of the kitas.

If you come here and work on a tourist visa and your employer is aware of this then thats your choice. The risk lies with you. It is illegal although it is also part of the process to obtain a working visa which makes it more confusing.

The time to get a working Kitas is anything from 1 to 6 months and the Kitas will be anything from 6 to 12 months.

So yes, you can find work if you look hard enough and you should find a school or a sponsor to ensure you are legal.

No degree = no hope of a work permit.
Citizenship can be applied for after 5 years living in the country without leaving for any reason, but the process will take around two years to complete, so 7 years in total.

Luke mentioned casual work.
That's unquestionably legal after 2 years of marriage and after getting your KITAP, but is only unlikely to be a problem on a KITAS.