i am trying to use CSS to change the color of headings of each post to Navy Blue and widget headings to Red.
You're close! The Under the Influence theme uses the h2 tag for post titles, not h1. Here is a CSS example that you can add to your Appearance → Custom Design → CSS editor that will turn post and page titles navy blue:
h2,
h2 a {
color: #000080;
}
The widget titles actually also use the h2 tag, so that rule should affect them as well. However, navy blue is hard to distinguish from black at small font sizes (at least in my opinion), so you might want to make those headings a little larger and use a different color for them. You could do it with CSS like this:
#sidebar h2,
#sidebar h2 a {
color: #152d99;
font-size: 1.3em;
}