You can move the trailing close quote image to a place some where inside your <p>
(you'll have to play with the positioning of it however; safe bet is about 10-15 words away from the end of the last sentence) So from your example you would have:
<div id="box1">
<div class="info">adfda</div>
<div class="post">
<img style="float:left" src="quotes-open.jpg" alt="" />
<p>lskg;alsjglkajg jlg; ;lkj g;lk aglkj;lgkjlkjg alkjs glkjhaslkj hjkas hglkj
asg hagl lskg;alsjglkajg jlg; ;lkj g;lk aglkj;lgkjlkjg alkjs glkjhaslkj hjkas hglkj asg hagl
<img style="float:right" src="quotes-close.jpg" alt="" />
lskg;alsjglkajg jlg; ;lkj g;lk aglkj;lgkjlkjg alkjs glkjhaslkj hjkas hglkj asg hagl
</p>
</div>
</div>
I think you'll have better luck with something like what Stephen suggested:
HTML:
<div>
<div class="info">adfda</div>
<div class="post">
<blockquote>
<p class="closeq">lskg;alsjglkajg jlg; ;lkj g;lk aglkj;lgkjlkjg alkjs glkjhaslkj hjkas hglkj asg hagl</p>
</blockquote>
</div>
</div>
CSS
.post blockquote { background: url(quotes-open.jpg) no-repeat top left; /*padding*/ }
.post blockquote p.closeq { background: url(quotes-close.jpg) no-repeat bottom right; /*padding*/ }
Notes
.post blockquote
: gets the opening quote set as a background and position to the top and the left. You'll want to adding some padding to the element so as to not crowd the text or overrun it.
.post blockquote p.closeq
: I went ahead and made it to where you have to explicitly tell where you want the closing quotes. This is because you may want a quote with more than one paragraph. Again here you'll want to play with the padding to make sure your text doesn't run over the closing quote.