Oil leaks are usually not a good sign when it comes to washing machines, regardless of the brand you own. A washing machine that drips oil will usually require a major part replacement to keep it running. Rather than repair your old Maytag washer, you might be better off upgrading to a new one if you find oil leaking from the bottom of the machine.
A common place for an older Maytag washing machine to leak is from the transmission. Maytag, along with other washing machine manufacturers, made design changes to their washers' transmissions after 1995 to limit the occurrence of oil leaks as the component wears. However, washers made before these changes were implemented are prone to leak. In general, once a transmission starts to leak oil under the washer, it must be replaced; a leaky transmission can't be repaired. The remedy will ultimately depend on whether or not it's leaking everywhere or just from the seal on the drive tube.
Drive Tube Seal
On the transmission's drive tube near its spline is a seal that prevents oil from leaking out of most Maytag washers. If the seal breaks, oil can empty out of the transmission from the bottom of the washer. Sometimes replacing a broken seal and adding more oil will fix the problem as long as the loss of oil didn't damage the transmission in other ways and cause certain components to cease. Contact Maytag to inspect the transmission and pinpoint the leak spot. If the technician determines that the transmission could be salvaged if the seal were replaced, swap out the faulty seal for a new one.
Like a washing machine's transmission, its motor also operates with oil and can develop a leak over time with normal use. Additionally, a leaky motor will deposit oil in the bottom of the washer's cabinet that will eventually end up on the laundry room floor. As the oil leaks out, the motor will lose some of its capacity to agitate and spin the washtub. Contact Maytag to request that a technician assess the motor's condition. If the leak is fairly minor, it might be repairable. However, if the leak has gotten so bad that the motor is severely damaged, consider purchasing a new washer.
Confirm that oil is leaking from your Maytag washer, not rust-colored water. Given that your washing machine is an older model, it's possible that water could be leaking from the washtub or water valve that might look like oil when in fact it's not. Although a rusty, leaky valve is repairable, a cracked washtub isn't and is expensive to replace.