Jay,
There?s no one port that your ancestors may have left from. There were sailings from Londonderry, Sligo and Limerick but by far the busiest departure port was Liverpool. It had more or less daily departures to the US and Canada, whereas from Londonderry it was about one or two a month. There was massive competition for the trade and shipping agents often included the cost of the ferry to Liverpool and accommodation there free, as part of the deal. Here?s a link to a site, which gives you a little background information. Though written in relation to the neighbouring county of Donegal, pretty well everything in the article would apply equally if you lived in Tyrone or some other part of Ireland in the mid 1800s:
http://www.finnvalley.ie/history/emigration/index.html
One of the agents for departures from Londonderry were J & J Cooke. They had sailings to Philadelphia, New Brunswick and Quebec, and their passenger records are kept in PRONI (the public record office) in Belfast, in date order. They start around 1847. They are not indexed, nor on-line as far as I am aware, and so you just need to work through them.
You ask about the impact of the famine in Tyrone. It certainly caused a lot of deaths, but just how severe depended on your circumstances. The smaller farmers and agricultural labourers (who would have a few perches of land) had rather rashly become one crop dependent (ie potatoes) and so were hit the worst. (You can grow more potatoes to the acre than any other crop and they require the minimum of maintenance. They also grow particularly well in Irish soil. So that?s why they were so popular). Bigger farmers grew a variety of other crops eg oats and hay, and those actually commanded good prices during the mid 1840s. The other source of income, mostly only available in Ulster, was money from linen weaving. Most farmers and labourers grew a bit of flax and turned it into linen which they sold for cash at the local market (probably Omagh in your case). So if you had other crops and a bit of linen money to fall back on, then you got through the famine.
But the famine wasn?t the sole driver for emigration at that time. Ireland has very few natural resources (no oil, coal, iron ore etc) and so did not benefit from the industrial revolution in the 1800s, the way Scotland, England, the US, Canada & Australia did, which created hundreds of thousands of comparatively well-paid new jobs in new industries (coal mining, steel making, ship building etc). So that was a big pull factor. There had also been a huge population explosion in Ireland going up from about 3 million people in 1750 to 8 million in 1830. There simply weren?t the jobs for all those people. In much of Ireland the only employment was subsistence farming topped up in Ulster and one or two other areas with a bit of linen weaving. And then the straw that broke the camel?s back, along came the famine, numerous times throughout the 1800s. The worst period was when the potato crop failed almost completely 3 years in a row in the late 1840s, and then partially several more years after that.
For a detailed description of what the area suffered, you should probably look at the Poor Law Records for Gortin workhouse (the area that included Droit). The minute books are kept in PRONI. The Board of Guardians met every week and the minutes generally record conditions in the area at the time. I have not seen the Gortin books but others that I have seen for the famine era in other counties in Ulster give good descriptions of what was taking place. So there are records how many people needed help from the workhouse (both indoor and outdoor relief), whether they were organising soup kitchens, and so on. It also records general information which is how I know that farmers growing other crops got good prices and managed to survive OK. In general, Ulster did not fare as badly as the rest of Ireland. In the years 1841 to 1851 the population of the whole island dropped by 20% (combination of deaths and migration) whereas in Ulster it was only 10%.
Other factors led to the continued emigration too, eg early mechanisation on farms. With new machines to turn the soil and plant seed, farmers no longer needed an army of agricultural labourers to help on the farm. So those jobs were rapidly disappearing. Likewise mechanisation had led to linen factories being set up in places like Belfast. These made home weaving uneconomic and so also upset the labourer?s family economy. Agriculture was the biggest single employer in Ireland, but it was mostly a barter economy. Few people had any ready cash save what they could make from weaving or any government sponsored work such as building new roads. So when the opportunity arose to get jobs with a regular wage packet, as opposed to a few pence from your father each week, the decision to migrate wasn?t really all that hard to make. So it was as much about economic betterment as anything.
There was just a massive tide of migration all through that century, including long before the famine. All the famine did was speed the tide up.
Elwyn