Below is what seems to be your current wire deignation.
It sounds as though you have a duel fuel type heating system .... heat pump / oil furnace. Your current thermostat has a 3rd heat control line .... the new one only has 2.
From what I can tell hooking the " O " and "W" wires together would be a bad idea.
The " O " wire is for the reversing valve for the cooling and the "W " is for the heat .... so hooking the 2 wires together sounds like it would have cooling and heating happening at the same time.
I'm no means an expert on heat pumps but it sounds like you might want to check with a HVAC contractor.
B - Heating damper motor; changeover valve
E - K Emergency heat relay
G - F Fan relay coil
L - System monitor
O - Cooling damper motor; changeover valve
R - Power connection to transformer (internally connected for heating
RC - Power connection to cooling transformer
RH - Power connection to heating transformer
W1 - H1, R3 Stage 1 heating control
W2 - H2, Y, R4 Stage 2 heating control
W3 - Stage 3 heating control (b)
(a) - Other terminal designations can be used that are not listed on this table. Refer to the hookup drawing and internal schematic for exact connections.
(b) - W3 controls the auxiliary heat like W2, and allows adding additional stages of auxiliary heat with outdoor thermo stats while maintaining the proper second stage anticipation.