You have 5V driving through R1 then D1 then R3 and D3 in one particular configuration of switches (SW1). If the LEDs drop 1.8 volt each this means 3.6 volts in total with R1 and R3 mopping up the remaining 1.4 volts (3.6 + 1.4 = 5).
Assuming you have 20 mA flowing through the LEDs (pretty standard sort of stuff), each resistor will be about 35 ohms.
This means that when SW1/SW3 is inactivated, OUTPUT1 will be at 5 volts. When either SW1 or SW3 are activated, 20 mA flows through R1 and OUTPUT1 = ~ 4.3 volts. This is your problem - you are not getting a decent low-logic level.
To remedy this you could consider using a comparator or a PNP transistor (this will also invert your logic level).