How large does an oven need to be to fit a 18 lbs turkey?
The oven in a standard 20" kitchen stove will accommodate a bird even as large as 20 lbs (9 kg).

The very detailed chart here, the pertinent details of which are replicated in the chart below, establish the standard dimensions of such an oven as 18 X 16 X 14.5 inches (46 x 41 x 37 cm).



In their downloadable Thanksgiving pdf, for a turkey as large as 20 lbs (9 kg) Williams-Sonoma recommends a 16 X 13 X 3 inch (40 x 33 x 7.5 cm) roasting pan. A pan of this sort is available with a rack which rises just above the bottom of the pan, as here and pictured below.



This kind of pan keeps height requirements down to roughly the height of the bird plus 3" (7.5 cm) above the bird, plus the standard 2.5" (6.5 cm) below the bottom rack. With 14.5" (37 cm) worth of oven height to work with and about a half inch space between the bird and the pan, that still leaves room for a bird 8" (20 cm) tall. (We won't expect the bird to be half as tall as the pan is long.) Meanwhile, an 18" (46 cm) oven depth accommodates a 16" (41 cm) long pan, and a 16" (41 cm) oven width a 13" (33 cm) pan width. Also, as seen here and below, the pan's handles fold down.



Now, none of this is to say that there's anything the slightest bit convenient about roasting so large a bird in so small a space. But it can be done. It should just be done with every whit of safety in mind.