It is never made clear if the ships in the Alien universe are capable of traveling at or above light speed. Wouldn't robotic or automated ships have been better-suited for such a long journey through space with cargo?
Yes, the ships are capable of speeds significantly above the speed of light. From in-movie clues this is fairly clear, e.g. from Alien dialog:
Then later in the meeting they have:
So the journey they are making is expected to take 20 months. A journey between stars below light speed would be years, decades or even longer. This isn't their 'local time' due to some relativistic effect of going at high sub light speeds, as Ellen Ripley is shocked when she finds that she slept for over 50 years between Alien and Aliens, and that her daughter had grown old and died.
In Aliens the Sulaco is dispatched LV-426 to investigate why the colonists had stopped communicating. Its clear its its to investigate and potentially rescue them ("its a bug hunt") and they find cocooned colonists, so its clear this is a fairly fast military ship.
I don't know where the information comes from, but the Alien v Preditor Wiki states that the speed of the Nostromo is 0.12 light years per day with its cargo.
As for the issue of automated ships being superior for such long voyages - this might be true, except that people are more adaptable and creative problem solvers - and putting your trust in people when you are ferrying huge quantities of (presumably expensive) oil might be seen as a good investment, even if they require more infrastructure to keep them alive than automation or androids.
Yes, either the ships can travel at theoretical speeds beyond that of light or they can enter and exit "warp" or "hyperspace" corridors which allow travel across vast areas of space in far less than time than traveling at or near light speed would. Some clues from the 19780 novelization of the film Alien and the subsequent Alien films are: