Agriculture: Goblins can do anything larger animals can't do. It shouldn't be too difficult to teach them to harvest crops, vegetables and fruit, take care of the plants in general, get rid of unwanted weeds etc.
Manufacturing can also be made easier. If they can clean, anything for textiles for example
- shearing sheep, spinning, weaving and so on - shouldn't be hard, and a lot more I'd assume. Later on they'd be ideal factory workers.
While their lacking strength can be a drawback, their stamina and size can also be useful in mining.
In general if goblins existed the way you describe them they'd be useful for almost anything at least in a support job. While they couldn't work as blacksmith themselves, for example, it wouldn't be a problem for them to operate the bellows, add coal to the furnace, clean and order tools and so on.
Other than typical work:
They can be employed as entertainment - circus, gladiator/pit fights, theater, possibly even music.
And, of course, they can be warriors. Give them spears, clubs and slings. They are faithful like a dog, but can handle weapons. Hell, they can even ride dogs for all I care... kinda depends on how uneasy domesticated animals get around them, but I'd consider it illogical to make dogs afraid of them if they live in the same household.
In other words, they'd be a part of every aspect of life and work. Nobody says no to a cheap and efficient worker.