have an 87 omni,what would cause back pressure in the cooling system ?

Nothing good. A little bit of antifreeze flowing back to the tank is alright but lots is not good. If it is excessive I would lean towards (or hope) the head gasket. Compression from a (the) clyinders is entering the coolant system and pressuring it up. Worst case It could be a cracked head or engine block. Check and/or drain your engine oil. If there is no water in the oil it should only be the head gasket. If there is then it is probably easier to source a used motor.

An '87 Omni with a blown head gasket! What are the chances?

As aforementioned, excessive pressure in the cooling system is usually typical of a blown head gasket. The head gasket is what seals the upper and lower halves of the engine together. When it leaks, you get combustion gases forcing their way into coolant passages, coolant being burned in the combustion chamber or oil mixing with the coolant (or any combination thereof). The motor can be evaluated with a compression tester (a gauge that screws into the hole where spark plugs go) and determine if the gasket is leaking combustion gases into the cooling system. This is a quick and relatively easy test, most gauges come with basic directions. Remove all four spark plugs. Disable the ignition system so the vehicle cannot start by removing the coil cable from the centre of the ignition cap and ground it to a point on the chassis out of the way. Screw the compression tester into the number one cylinder and with the aid of an assistant, have one person check the gauge while the other cranks the engine over. Open the throttle wide open while cranking. Let the motor turn over for several compression cycles and watch the gauge. It should shoot up fast and eventually stabilize at a reading. Most engines read between 140-150 psi(g). Repeat this for all cylinders. The difference between the highest and lowest reading should be within 10% of each other. If one cylinder is very low or if two adjacent cylinders are low it is usually indicative of a blown head gasket.

Like above , but get the head checked for warpage

Take the head off and check the triangular coolant passages. Those heads crack there and the cracks run towards combustion chambers.