She's alone in the house tonight as the rest of her family has gone out.
I like to be alone sometimes.
Sometimes, we use 'on my own' instead.
You shouldn't go out on your own at this time of night.
These following sentences are all correct:
Sheila prefers running on her own.
Sheila prefers running alone.
Sheila prefers running by herself.
If I say I'm lonely, however, I feel unhappy because I'm alone, or because I have no friends.
Wikipedia: One way of thinking about loneliness is as a discrepancy between one's desired and achieved levels of social interaction.
So, you could be in a room full of people, but yet feel lonely because no one is talking to you.
Sarah feels very lonely after her husband left her.
Lonesome is a synonym for lonely, although it's more common in US English.
Remember Elvis? Are you lonesome tonight? Do you miss me tonight?
Listen to this tremendously moving song by Ben Harper.