Some seeds are more viable than others, and as has already been said it depends upon 'how they are kept'
Datura & Jacaranda;.... Datura is quite a hard seed as I recall, so I think it should be OK in second year. I don't know anything about Jacaranda.
Sweet Corn should be OK.
My method of sowing/storing.
If the packets contain more seed than I require I sow as follows;
Year 1; I sow about a third of a packet, and more often that not I get fairly good germination.
Year 2; I sow the other two thirds, and assuming I only get 50% germination this is similar to the year before.
There are some seeds that I have had for three or four years. These are generally fairly large seeds that I sow individually so don't use as many each year.
These are generally brassicas, so in succeeding years I always sow a few more than I need to allow for poorer germination results.
e.g. year 1=12 seed >>> year 2=20 seed >>>year 3=30 seed in the hope of getting 10 each year, and it works pretty well!