* Elderly: aged, senior, old, mature, senile (if referring to a decline in mental abilities)
* Old: aged, senior, antique (for the cat), veteran (for the cat)
* Live: reside, dwell, inhabit, stay, occupy
Here are some ways you could rewrite the sentence using these synonyms:
* Misa's aged aunt and her senior cat live down the street.
* Misa's senior aunt and her veteran cat reside down the street.
* Misa's mature aunt and her antique cat dwell down the street.
The best synonym to use will depend on the specific context and the tone you want to convey.