How to create different margins for odd and even pages?

LaTeX uses different margins on odd and even pages only if the twoside option is activated in the \documentclass line.

With the geometry package it's fairly easy to adjust the page setup parameters. For example

\documentclass[a4paper,twoside]{article}

\usepackage[
  inner=<XX>pt,
  textwidth=345pt,
]{geometry}

would set the usual "oneside" textwidth. Choose the value for <XX>pt to suit your needs. Check the manual of geometry for other options, in particular for setting the text height.

Spacing between paragraphs can be due to big indivisible objects near the end of a page. If there are many short subsections, this may happen, or if there are big math displays. Curing the appearance is a job to be done when the text is in final form.

A \raggedbottom command before \begin{document} will avoid this, at the expense of having non even page height.

Often we use different margins on odd and even pages for double-sided printing. It allows us to knit documents. I use GOST layout:

\documentclass[a4paper,12pt,twoside]{article}
\usepackage[inner=3cm,outer=1cm]{geometry}

If you remove twoside parameter you get classic layout for one-side printing.

LaTeX just uses the odd side settings unless you specify the twoside option to the class.

\documentclass[a4paper,12pt,twoside]{article}