There are a few issues with your CSS. You did not close your <ul> element and the width of the <ul> is so small that it is squeezing the <li> elements into a single column. You have also mixed up your CSS selector syntax. Instead of .socialicons ul it looks like what you want is .socialicons.
There are really only rare cases that you should use descendant selectors. CSS is parsed from right to left. See here for more about this: http://css-tricks.com/efficiently-rendering-css/
http://cssdesk.com/D8xrT
HTML
<div class="social">
<ul class="socialicons">
<li id="facebook"><a href="#"><img alt="Facebook" src="http://placekitten.com/g/24/50" width="24" height="50" /></a></li>
<li id="twitter"><a href="#"><img alt="Twitter" src="http://placekitten.com/g/30/50" width="30" height="50" /></a></li>
</ul>
</div>
CSS
.social {
position: absolute;
right: 1.5%;
top: 5px;
width: 75px;
}
.socialicons {
list-style: none;
display: inline;
padding-left: 0;
padding-bottom: 0;
}
.socialicons li {
display: inline-block;
padding: 0.3em;
float:left;
}
.socialicons ol, ul {
list-style: none;
display: inline-block;
}
.socialicons ul a {
display: inline-block;
text-decoration: none;
}
.socialicons img {
max-width: 50%;
height: auto;
}