Very interesting. I pulled up my 8087 book "THE 8087 PRIMER", John F. Palmer and Steven P. Morse and looked up rounding. The nearest to what you described is the "round to nearest Even" mode, not the round to the nearest Odd as you described. Are you sure about this? Is it in some C spec?
If you are programming the FPU and want to cast a float to an integer, you just execute an FIST or FISTP, which will round to the specified rounding mode which is usually "round to nearest Even" unless you specifically set the mode to "round to 0" before you store the value.