Translation:I did a lot of work and got tired.
which is weird because that's the correct way of saying it the other times.
"because" will require us "から" I think. So the sentence will be. たくさんしごとをしてから。つかれました。Feel free to correct me!
You can use から to mean "because", but you can also use the -te form of the verb like in this sentence to imply a cause and effect relationship.
It basically means the same thing. If it's not accepted, I think it's because the Japanese says 仕事をして (shigoto o shite), where して is from the verb します (shimasu) meaning "to do". The Japanese is specifying that the subject of the sentence has done work and has become tired, while your translation has no action and is just saying that work made the person tired.
You could put a comma there. Japanese comma usage isn't as defined as in English, so it's also fine not to use a comma.
Is it OK to say しごとして without を ? In other sentences I remember that only しごとします is written.
You're remembering correctly. しごとします (shigoto shimasu) is a verb that means "work". This sentence is actually a little tricky, because it's saying "I did a lot of work", where the verb is "did", not "work". In this case we should should use しごとをして to say we "did a lot of work" (たくさんのしごとをして takusan no shigoto o shite).
(*Note that in casual speech it is absolutely okay to drop particles.)