I supplying the oil refinery with oil from a nearby oil rig by train but my lorry station next to the refinery is not creating any goods to transport.
First, check whether the refinery is actually producing goods -- you can click on it and get a window saying "XXX goods produced last month (Y% transported)".
Second, and this is important, goods will only start arriving at the station after the first vehicle capable of carrying goods has stopped at that station for a pickup.
Something else that is important to consider: Make sure that your goods station has the generating tile for the industry within its catchment area.
A station can accept things iff it has 8/8 (or more) worth of 'acceptance' for that cargo. A tile can provide fractional acceptance. Industries usually have several tiles providing the full 8/8. This means it's possible to have some of the Oil refinery in your catchment area without being able to deliver oil to it.
When a station has multiple bounding boxes, the area in-between is also counted for acceptance. This is important for more complex or disjoint stations.
You can take away anything as long as the smallest bounding box for the industry overlaps any of the bounding boxes of your station's catchment area. Note that this is diffrent from the acceptance calculation. Tiles in-between bounding boxes are not counted here.
An example of a case where you can deliver, but not take away is this situation. Tiles inbetween the two stations cover the 'deposit' tile for the Oil Refinery, so you can deliver oil there. However, you cannot pickup any Goods, as the bounding boxes of your station's catchment area do not overlap the bounding box for the oil Refinery.
This page on the wiki has some more examples.