"There is room around where the washer drain hose fits into the 1-1/2" drain pipe for air to be pulled in when the washer drains."

That has nothing to do with plumbing venting.

Venting is to allow the water to flow in the waste lines without creating suction that could empty the traps used to keep sewer gas from entering your house.

You know that gurgle the toilet makes as it flushes?

That is desired in that case sine the water in the bowl is restored as the tank fills.

If that happens on other drains there is nothing that will refill the trap.

The washer might, depending on the applicable code, be able to vent with a Studor vent. Check the code for that specific location.

There are many rules about venting under each of the plumbing codes.
It is not easy to advise.
After (downstream of) the P trap at the bottom of the stand pipe, a vent is required under every code I know of.
Other rules apply too.
For example, there are limits on what other fixtures' drains can be plumbed onto that same Trap arm.

A washer's stand pipe is an "open" drain which will gurgle.
It must be open. Not closed.
This is entirely not the same thing as a vent.
A vent (in DWV terms) is always on the downstream side of the P trap.

http://www.terrylove.com/forums/index.php has forums for various plumbing codes.

hth