My landlord owns the house. I share an apartment in the house... on in which I have my own separate entrance. My rent is very fair and my landlord is fair but
Cheap. Anyway, I chipped in w/him to fix my oven which is 50 years old. It broke again so I bought a portable oven and didn't ask to fix this old one.

I want to install a new oven at my own expense. Can I do it without his
Permission.

Also, if she sells the house, do I have any rights to stay? I haven't had a lease in eighteen years.

Landlord tenant laws go by state (in the US) so please say where you are.

In general:
"I want to install a new oven at my own expense. Can I do it without his permission." - No, because an oven (stove or range vs cooktop and oven) requires wiring to code, and you don't know if the old wiring is adequate for a new appliance drawing that much electricity or if the plug will even be the right one. Also, aren't you on good terms with the landlord? Just ask!

"Also, if she sells the house, do I have any rights to stay? I haven't had a lease in eighteen years." - You have very limited rights to stay after being given proper notice in writing, ranging from 15 days to 60 days, depending on where you live.

ANY question on law needs to include your general locale as laws vary by area. Without a lease you are a month to month or periodic tenant. That gives you the right to whatever notice is required by local law. It can be anywhere from 15 to 60 days depending on where you are.

You do not have the right to install any permanent fixture (and a stove is considered a permanent fixture, without the landlord's permission.

The issue with oven, it becomes part of the house, and that you may have a right, to require him to fix or replace the old one. If you rent, it is OK to make some demands.

If he sells house ( is he talking about it) just normal notice is needed to evict you

I live in one of the five boroughs of New York

ANY question on law needs to include your general locale as laws vary by area. Without a lease you are a month to month or periodic tenant. That gives you the right to whatever notice is required by local law. It can be anywhere from 15 to 60 days depending on where you are.

You do not have the right to install any permanent fixture (and a stove is considered a permanent fixture, without the landlord's permission.

I live in New York

In NY if you are a month-to-month tenant (as in this case where you don't have a written lease) the landlord must give you one month's notice to move out. So a future landlord, or your current landlord for that matter, can ask you to vacate the premises with one month's notice.

I agree with the previous posters - you may not install a permament appliance (of make any other permanent changes to the apartment, such as remodeling the kitchen or changing bathroom fixtures) without the owner's permission. In this case since you're on good terms you may be able to bargain with him - perhaps you pay for the oven in exchange for a month's rent.

I was going to pay for a new oven to begin with. I see now that I can't just do it, I will speak with him first. Thank you.