The walking part isn't odd, though we do wonder about your luggage. We'll assume you're an inveterate backpacker and carry all your travel belongings on your back.
The challenge isn't so much the distance from the airport to the Strip. According to Google maps, it's only 2.5 miles from the airport to Excalibur. Google suggests 51 minutes, which is a typical 20-minute mile; your mileage might vary, depending on your own pace and, again, the weight you're hefting.
The problem is more that the airport is designed for anything but walking to and from. The sidewalks peter out at the end of the main terminal building and then you've got more than a half-mile of lane crossings, overpasses, and general heavy Las Vegas traffic -- lead-foot cab drivers, visitors in rental cars, buses and shuttles, limousines, all jockeying for position, with a luggage-toting pedestrian the farthest thing from their minds.
Not that it can't be done, of course. In our many many trips to and from the airport, we have seen, though on rare occasions, pedestrians on foot, wheeling suitcases to and from, though admittedly they looked a little bewildered. As always when hoofing it around traffic, if you're especially cautious and patient, you'll probably make it. (A good idea, however, might to be make sure your life insurance is paid up.)
So you follow the one-way traffic past the terminal building and out onto Wayne Newton Boulevard for approximately four-tenths of a mile. The most dangerous part is where Wayne Newton crosses over Paradise Road; there's no shoulder and you're jammed in between the guard rail and the traffic. But once you're on the other side, you join up with Swenson Street, which has a nice wide sidewalk and you're pretty much home free. You can continue north on Swenson till you hit E. Tropicana, or you can cut west on one of the cross streets; you'll pick up Paradise Road (heading against traffic), where you take a right to head north again to E. Tropicana. In total, it's roughly a mile from the terminal to E. Tropicana.
From the intersection of Swenson, it's one and a half miles to the Strip. From the intersection of Paradise, it's 1.3 miles to the Strip.
