After a couple hours, I think I have a pretty good plan, so here goes...
So, you have just been given control of the US Postal Service, with the goal of invading Canada.
The Postal Service lost 15.9 billion dollars last year, and is overall very inefficient. The first step would be to significantly reorganize the agency to reduce costs as much as possible. On paper you would not report a reduction in costs, and the excess money would be discreetly set aside for the invasion.
Some background: The postal service operates 211,000 vehicles, 140,000 of which are the mail trucks you see everywhere. This is the largest 'civilian' vehicle fleet in the world. In addition, there are 617,000 active employees.
The postal services of the US and Canada have many special privileges, such as sovereign immunity, powers of eminent domain, and the ability to negotiate postal treaties with other nations.
Over the following years, the USPS would negotiate a postal treaty with Canada that would loosen border security for both countries' postal services, and if possible to allow trucks free access to Canadian roads.
As for the invasion itself, the force has to be big enough to defeat the majority of the Canadian Ground Forces. There are just over 50,000 in-service and reserve soldiers.
The USPS would discreetly acquire weapons, armor, and explosives. Assuming everyone working there is in on the plan, a large number of able-bodied staff would receive military training.
This probably wouldn't be enough since many mailmen/mailwomen would be too old or too out of shape to efficiently train. So, addtional efforts to recruit/hire young men and ex-military personnel would eventually get you about 200,000 trained 'soldiers' (They would be less skilled than active military personnel, so I'm assuming just to be safe that 100,000 mailmen with military training could face off against 50,000 actual soldiers, with another hundred thousand in reserve).
Some of the trucks will be fitted to bring troops, while others will become suicide bombers- more on that later.
**The Targets**
The goal of the invasion is to capture the capital and reduce as much as possible the military's ability to retaliate. Normally the US would be there to help out, but when confronted alone Canada will be much easier to invade. The targets are Ottawa (obviously) as well as 3 other military bases. One, located outside of Ottawa (North Bay), is a major communications center, but has no airfields. The other two bases (Cold Lake and Bagotville) are farther from the border, but have fighter aircraft. 79 CF-18 Hornets are kept at these two bases- this comprises the entirety of their armed aircraft. A surprise attack on both bases will give access to them, granting a major advantage.
As for anti-aircraft defenses, Canada has an arsenal of 20 anti-aircraft guns and 36 anti-aircraft missile defenses. Although very effective against aircraft, in a surprise attack they will be much less effective. In addition. the anti-aircraft guns used, have an effective firing range of 4 km, and the ADATS missile used have a max height of 10km. The jets being hijacked can fly at an altitude of at least 12km, so they will be vulnerable only when taking off and attacking.
**The Strategy**
The main advantage here is sheer numbers and the element of surprise. For each military base, several thousand trucks will make their way into Canada. For Cold Lake, trucks will enter through northern Montana and travel 450 miles north to the base. For Bagotville, the crossing is near Dennistown, Maine, 230 miles south of the base. The trucks attacking North Bay will cross the Lewis-Queenston bridge, right next to Niagara Falls, then drive 300 miles north.
The main invasion force is much larger, and is harder to hide. The trucks will enter over a long period of time through a variety of locations along the New York/Canada border, each hiding in the forest and laying low until all trucks are ready.
The attacks will start simultaneously. For the aircraft bases, several trucks with explosives will detonate around the perimeter, at the main gate, and near select buildings. It is important that the aircraft as well as fuel reserves remain unharmed, so only infantry will be used after this point. The remaining soldiers will be vastly outnumbered. After the majority of the base is taken, ground crews will be brought into the base and will begin preparing and refueling the jets. Once the base has been captured, pilots (trained extensively to fly the jets in simulators) will enter. They are not expendable, so it is important the base is secure before they come in.
Since the goal for North Bay is just to destroy it, an even balance of infantry and suicide bomb trucks will be used.
The rest of the ground force will attack Ottawa. Explosives will be used on bridges and other infrastructure in the surrounding area to slow reinforcements. The infantry will converge on the government buildings, taking all everyone present hostage.
The jets will be extremely useful in the following hours. Without the help of the US and stripped of its fighter jets, Canada will have no way to deal with the jets. The first jets to take off from Bagotville will fly to Ottawa to support the invasion. At mach 1.8, they will arrive 15 minutes after taking off, no more than an hour after the start of the invasion. The other jets will be focused on destroying all other military bases and any stocks of tanks or artillery which would be used to take back the city.
The result would be a near-complete defeat of the Canadian armed forces and complete control of the capital. From there, the US Postal Service could use its military dominance over the rest of the country to bring it under its rule.