Is silicon dioxide more acidic than the oxides of nitrogen?
I think your question boils down to:

What is the meaning of acidic strength of oxides? How do we determine the acidic strength of oxides? 

In general, the electropositive character of the oxide's central atom will determine whether the oxide is acidic or basic. The more electropositive the central atom, the more basic its oxide. The more electronegative the central atom, the more acidic its oxide.

Electropositive character decreases from left to right across the periodic table and increases down a group.
The trend of acid-base behaviour is from strongly basic oxides on the left-hand side to strongly acidic ones on the right, via an amphoteric oxide (for example, aluminium oxide) in the middle.

This trend applies only to the oxides of the individual elements  in the highest oxidation states for those elements. The pattern is somewhat less clear for other oxides.

A non-metal oxide's acidity is defined in terms of the acidic solutions formed as a result of reaction(s) with water. For example, sulfur trioxide reacts with water to forms sulfuric acid.  

In general, acidic oxides are oxides of nonmetals and basic oxides are oxides of nonmetals.

Note: There are three nonmetal oxides from the upper right portion of the periodic table, $\ce{CO}$, $\ce{NO}$, and $\ce{N2O}$, which have low (not the highest possible) oxidation numbers for the central atom that they give neutral aqueous solutions.

Since the acidity of a cation rises rapidly with charge, d-block elements which exhibit a wide variety of oxidation numbers may have one or more oxides that exhibit only basic properties and one or more oxides that exhibit only acidic properties.

In general, the higher the oxidation number, the more acidic the corresponding oxide (similarly, reverse trend for basic character of oxides). Chromium makes a decent example here, as it exhibits a variety of oxidation states. $\ce{CrO}$ is basic, $\ce{Cr2O3}$ is amphoteric and $\ce{CrO3}$ is acidic.



P.S. 
Let me introduce you to a theory developed by Hermann Lux and Håkon Flood, named Lux-Flood theory to explain the acidic or basic character of oxides. Here's what they had to say:


  An acid of Lux-Flood is an acceptor of $\ce{O^2-}$
  A base of Lux-Flood is a donor of $\ce{O^2-}$


For example:

$\ce{CaO}$ is a base of Lux-Flood because $\ce{CaO}=\ce{Ca^2+}+\ce{O^2-}$

$\ce{SiO2}$ is an acid of Lux Flood because $\ce{Si}$ has vacant d orbitals, allowing it to accept more $\ce{O^2-}$ ions. 

The two compounds may react to give you $\ce{CaSiO3}$.