I'm old-fashioned. I think that a list of links should be normal weight, blue, underlined. So I created some in HTML code and pasted that into a Widget "Text" on the sidebar. But it displays as the theme's default color, bold, no underlining.

Is there some way I can force these links to display the way I've coded them?

You can access, through HTML/CSS Inserts -> CSS Inserts:

all text widgets

div.widget_text a:link,
div.widget_text a:active,
div.widget_text a:visited,
div.widget_text a:hover {
color: #123456;
font-weight: normal;
text-decoration: underline;
}

a specific text widget:

div#text-368010091 a:link,
div#text-368010091 a:active,
div#text-368010091 a:visited,
div#text-368010091 a:hover {
color: #123456;
font-weight: normal;
text-decoration: underline;
}

The ID text-368010091 is different for each text widget, and yours will most likely have another number. You'd have to look this up in the source code of the browser-rendered page, or with Firebug.

For all links inside list items inside widgets:
See Atahualpa Theme Options -> Widgets

For all links in the sidebars:

td#left a:link,
td#left a:visited,
td#left a:active,
td#left a:hover,
td#right a:link,
td#right a:visited,
td#right a:active,
td#right a:hover {
color: #123456 !important;
 font-weight: normal !important;
 text-decoration: underline !important;
 }

I've added !important here as otherwise it might not be able to overwrite all widgets

thank you for the info. very helpful.