Q:

What is the correct Orientation of Earth's Rotational-axis w.r.t Ecliptic at Equinox?

I am boggled with the position of earth relative to the sun at the "Equinoxes". 
According to the wikipedia:

an equinox occurs twice a year (around 20 March and 22 September), when the tilt of the Earth's axis is inclined neither away from nor towards the Sun, the center of the Sun being in the same plane as the Earth's equator.

My confusion starts from here: if earth's rotational-axis is neither tilted towards nor away from the sun then it means that celestial-equator and ecliptic become parallel to each other at equinox.  But which is, of course, ridiculous because it would mean that earth's rotational axis's tilt of $23.5^o$ reduces to $0^o$ at equinox. 
If above is not true then what is the exact orientation of the earth in space at equinox? 
Help in the matter will be highly appreciated.

A:

At the equinox the earth rotation axis is in a plane that is
tangential to the planet orbit, and orthogonal to the orbital
plane. Hence it cannot be tilted towards the sun or away from it.
But it does not mean that it is not tilted, but simply that (assuming the axis
has an orientation) it is tilted forward, or backward, on its path
around the sun. And since it is tilted, the celestial equator and
ecliptic are not parallel.
By the way, if it is oriented towards the sun on one solstice and away
on the other, it has to go through intermediate positions. Actually, the axis keep approximately the seme orientation (with respect to stars) all year long, up to precession.

