From what I can see from your photos, the hull looks good. Are the deck plates salvageable? If not, you will need to decide whether or not you are going to replace them, and if so, whether you are going to use inset or on-laid deck plates. Obviously, inlaid deck plates require more work and fitting, not only shaping of the plate itself, but of the ends of the inwales where they meet and join at the stem. With on-laid deck plates, the ends of the inwales need not join up precisely and the plate simply needs to be shaped and contoured, then screwed onto the tops of the inwales.
I have rerailed canoes with ash, but not with oak. With ash, there is usually no need to steam bend the inwales and outwales. Oak may be different, however, and the Winooski is a short and rather wide canoe and there is going to be a good bit of convexity of the outwales, and concavity of the inwales, so you might have to. I would suggest starting out on the assumption that you won’t need to steam the wood, but if you find during the installation that the inwales or outwales don’t want to cooperate, you could probably just steam a third of the length or so at each end. I have seen descriptions of some inexpensive steam chambers made from PVC pipe for this purpose. There are a number of forums for wooden boat construction and repair that contain a wealth of information that might be helpful.
Here is a link to a pdf file from Mad River Canoe on gunwale repair and replacement that I think you might find helpful:
Before you remove the remnants of the existing gunwales from the boat, mark on the hull the positions of the center thwart, the seats, and the end carry handles. Also use the center thwart to get an accurate beam measurement for the hull. Most Winooskis I have seen have had a center carry yoke instead of a straight thwart so it is possible that center thwart is not stock. Use it to brace out the hull sides, then measure your beam at center. MRC listed a gunwale width of 39" at center and they usually took this measurement at the outside edge of the molded hull, i.e, the beam measurement not including the outwales. Save that center thwart and use it to jack out the hull to its proper width as you start to fit your gunwales. Typically the hull will collapse inward without the rails. If you install your gunwales and then try to jack the hull out to spec you will be applying stress on your gunwale screws as well as to the inwales, outwales, and the holes in the hull that the screws go through.
If you need to lay up multiple pieces to achieve sufficient length (in your case about 15’ for each stick) I would use simple scarf joints which should be easy for you, having woodworking experience. A lot of builders suggest a long scarf in a 1:7 ratio (thickness to length) or longer. That might be necessary to provide a sufficient bonding area when scarfing thin panels but I have used much shorter scarfs of 1:3 and been quite happy with the results. With inwales and outwales of approximately 3/4" thickness a shorter scarf will still provide plenty of bonding surface. I use epoxy to bond the scarfs together. Arrange your scarf joints to that the joints on the inwales and outwales do not overlap if possible, and so the scarf joints point backwards at the outer edges of the outwales and inner edges of the inwales.
You will need to decide whether you are going to “sandwich” the inwales and outwales so that the tops align with the top of the hull, or whether you are going to route the outwales so as to leave a thin lip or kerf that covers the top of the hull. The latter is what is usually done with composite hulls, and looks a bit more elegant but requires more work. If you have a table saw with a router blade or a router table you may be all set up to route the inwales. Definitely route the outwales rather than the inwales as you want to preserve the full width of the inwales to mount your seats and thwarts.
Fitting the inwales will be the harder job because the length must be precise and the joinery at the ends needs to be decent, if you plan to use inset deck plates. Before you start to install the inwales you need to drill the holes for your gunwale screws and countersink them. Leave the ends long initially and start to attach the inwales at the center point of the hull, using some scrap wood on the outside of the hull to catch the screws if necessary. You can leave the ends sticking out over and above the stems at each end of the hull. Make sure you have the hull jacked out to proper width. You will probably be able to continue to attach the inwales to the hull for some distance from the center before it becomes necessary to trim and fit the ends. Once you get the first inwale temporarily installed, fitting the second inwale becomes easier.
When installing inwales and outwales I use inexpensive plastic spring clamps to hold the wood against the hull. Pad the wood to avoid leaving marks. I have found these to work as well as any other method I have tried.
Once you have inwales installed you can start installing the outwales. Remove a few inwale screws near the center, and start installing the outwale at the center point. Use clamps to hold the inwale and outwale tightly together as you drill your pilot holes in the outwales and alternate ends as you install each additional screw. Since the thickness of the hull will likely vary along the length of the boat, you may need to trim the width of your lip or kerf in you chose to route the outwales. Again, leave the ends of the outwales long. These can be trimmed after the outwale is nearly completely installed. After you get the inwales and outwales installed, you can trim and fit your deck plates.
For finishing, you can either use a “penetrating” oil on the rails, or a bright finish. There are advantages and disadvantages to both. I treat the inner surfaces of the inwales and outwales (the faces that face the hull) with a low viscosity “penetrating” epoxy even if I choose oil the other faces. If I use a bright finish (varnish or polyurethane) I will usually apply a couple of coats of low viscosity epoxy to the wood first. Whole manuscripts have been written about varnishing strategies. You can find a lot of info on the wooden boat forums. The most popular choices for marine varnish seem to be Epiphanes and Pettit Z-Spar.
You can find replacement seats, thwarts, carry handles, and yokes at Ed’s Canoe or Essex Industries:
I would plan to replace the straight center thwart with a carry yoke. You will probably need an extra wide bow seat for the Winooski unless the existing seat is salvageable. You can easily refinish and recane the seat if the wood is sound. You definitely need stainless steel machine screws (#10 size with either 24 or 32 threads per inch) for your yoke, carry handles, and seats, and finding long ones for the seats can sometimes be tricky so if you order from Eds you may want to order a set of 8 long 10x24 machine screws as well. You can make seat hangers out of hardwood dowels if you wish, or you can buy truss seat hangers from one of the above vendors.