Jocelyn,
There are no passenger records for travel from Scotland to Ireland. It was a short domestic journey and no records have ever been kept. (North Island to South Island in New Zealand. That sort of journey). Passenger records were really only ever compiled for inter-continental journeys eg to America or New Zealand. Domestic journeys or travel to France etc did not normally generate passenger lists.
Going back over the information you gave previously, I see that you found a death for Jane Woods in 1871 aged 30. Is it this death?
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1871/020774/7287686.pdf
If so, I don’t think it’s the right Jane Woods. That lady was still married (not a widow) and her husband was a gas-fitter, not a labourer. She lived in Sion. I suspect her husband was Patrick. Likewise I don’t think the other 1871 death is right either. This is it:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1871/020760/7283259.pdf
That lady was also still married (probably to Thomas Woods) and she lived in Newtownards which is about 100 miles from Strabane. I can see that it is on a number of trees on a tree on Ancestry. I would say it is simply wrong.
This 1874 death looks to me to be more likely. The age, location, marital status and husband’s occupation all fit:
https://civilrecords.irishgenealogy.ie/churchrecords/images/deaths_returns/deaths_1874/020644/7242806.pdf
That would have Jane born c 1834, the same as James. That fits much better. You might get a little more information about her from the workhouse admission records which fortunately have survived. They are in PRONI in Belfast. Who was looking after her children I wonder, or were they in the workhouse too? Information on Strabane Workhouse here:
http://www.workhouses.org.uk/Strabane/
If you are unable to go yourself, you could employ a researcher. Researchers in the PRONI area: http://sgni.net
I had a look at the trees on Ancestry. There are 27 with this family but they nearly all repeat the same information, so people have just copied someone else’s research. Many have James parents as James b 1822 and Catherine McGery (McGairy) b 1823. A moment’s reflection should have them realise that cannot be correct, but evidently that didn’t happen. (The parents would have both been 10 when James was born). Someone’s been guessing and others have slavishly copied it. You do see a lot of poor quality research on some trees. Or to use the correct technical term, utter rubbish.
I have a little information for you. There is a baptism on 17.3.1862 in the RC parish of Ardstraw East for James Woods, to James & Jane. The baptism entry is noted “Gordon a protestant”. So you know from this that Jane was protestant (if from Scotland then statistically she's likely to be Presbyterian) and that James was Catholic.
https://registers.nli.ie/registers/vtls000632983#page/8/mode/1up
Ardstraw East’s records only start in 1860. So my guess is that James & Jane married there c 1859 (if daughter Sarah Jane was born in 1860). And that’s why you can’t find the marriage record. It doesn’t exist. Likewise if it’s where James comes from, there are no baptism records for the 1830s so it will be virtually impossible to know who his parents were.
Finding Jane’s origins is also going to be virtually impossible, especially without parents names. I searched the Scotlandspeople site for Presbyterian births for Jane Gordon 1830 – 1838. There are 100, spread across Scotland from the Borders to Inverness. Take your pick.