Ok, firstly yes you can use JavaScript with ASP.NET but doing things the way you have done them isn't really the way we do them in ASP.NET. You should always take advantage of built in features in order to speed up development time as well as other built in functionality you get for free, which I'll explain later.
Firstly I have removed all of your JavaScript, I have kept 99% of your form but I have added to it and you should keep your server side ASP.NET code. Instead of writing JavaScript to validate a field I have simply used validation controls which will do the work for us. Here is the code (don't worry it isn't as confusing as it may first seem):
<asp:panel id="pnl_form" runat="server">
<form id="form" runat="server">
<table id = "contactform">
<tr><td>Name:</td><td><asp:textbox id ="strName" runat="server"/><asp:RequiredFieldValidator runat="server" ID="rfvstrName" ControlToValidate="strName" Display="Dynamic" ErrorMessage=" You must enter your name" /></td></tr>
<tr><td>Email Address:</td><td><asp:textbox id="strEmail" runat="server"/><asp:RequiredFieldValidator runat="server" ID="rfvstrEmail" ControlToValidate="strEmail" Display="Dynamic" ErrorMessage=" You must enter your email address" /><asp:RegularExpressionValidator runat="server" ID="revEmailPattern" ControlToValidate="strEmail" ValidationExpression="^([\w-\.]+)@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.)|(([\w-]+\.)+))([a-zA-Z]{2,4}|[0-9]{1,3})(\]?)$" ErrorMessage=" The email address you have entered is not valid, please enter a valid email address." /></td></tr>
<tr><td>Website:</td><td><asp:textbox id="strWebsite" runat="server"/><asp:RequiredFieldValidator runat="server" ID="rfvstrWebsite" ControlToValidate="strWebsite" Display="Dynamic" ErrorMessage=" You must enter your website address" /></td></tr>
<tr><td>Subject:</td><td><asp:textbox id="strSubject" runat="server"/><asp:RequiredFieldValidator runat="server" ID="rfvstrSubject" ControlToValidate="strSubject" Display="Dynamic" ErrorMessage=" You must enter a subject" /></td></tr>
<tr><td valign="top">Your Message</td><td><asp:textbox id="strYourMsg" runat="server" Columns = "30" Rows = "10" TextMode = "MultiLine"/><asp:RequiredFieldValidator runat="server" ID="rfvstrMessage" ControlToValidate="strYourMsg" Display="Dynamic" ErrorMessage=" You must enter your message" /></td></tr>
<tr><td></td><td><asp:button id="btnSubmit" runat="server" Text="Submit" OnClick="submitQuery" /></td></tr>
</table>
</form>
</asp:panel>
<asp:panel id="strMessage" runat="server" visible="false"><p>Thank you for your enquiry, I shall be in contact shortly.</p></asp:panel>
Consider this line:
<tr><td>Name:</td><td><asp:textbox id ="strName" runat="server"/><asp:RequiredFieldValidator runat="server" ID="rfvstrName" ControlToValidate="strName" Display="Dynamic" ErrorMessage=" You must enter your name" /></td></tr>
This is your TextBox for the users name, you'll see I have added a RequiredFieldValidator control to it. A RequiredFieldValidator does exactly what it says, it ensures the field has data in it before allowing the form to be submitted to the server (the JavaScript is created automatically when the page is built, this is why you don't need to write the JavaScript for it).
The two important attributes are ControlToValidate and ErrorMessage. Now ControlToValidate is used to tell .net which control this validation control is for, in this case it's your strName TextBox, so this is the TextBox it is going to be working with. ErrorMessage is simply the error message you want to display to the user should validation fail, in other words if they left the TextBox empty this message will be displayed to them.
You'll note I've added a RequiredFieldValiator to each of your controls, so in this scenario all controls must be completed before the form can be submitted. Note that I have also added another validation control for your strEmail TextBox called RegularExpressionValidator, here it is again:
<asp:RegularExpressionValidator runat="server" ID="revEmailPattern" ControlToValidate="strEmail" ValidationExpression="^([\w-\.]+)@((\[[0-9]{1,3}\.[0-9]{1,3}\.[0-9]{1,3}\.)|(([\w-]+\.)+))([a-zA-Z]{2,4}|[0-9]{1,3})(\]?)$" ErrorMessage=" The email address you have entered is not valid, please enter a valid email address." />
Again you'll see the ControlToValidate attribute and it is pointing at your strEmail TextBox. Also you'll see the ErrorMessage attribute. There is the ValidationExpression attribute which looks like I've had a few too many but what it does is simply ensure the user enters a real email address before allowing the form to be submitted.
There are a few more validation controls available to you including a CustomValidator which you can use to write your own JavaScript for instances where the built in validation controls aren't up to the job, but you should always stick with the built in ones when they are. Also there is a ValidationSummary control which can be used to display all the errors in one group anywhere on the page as opposed to next to each control as I have done here.
The advantage to using validation controls are many, firstly, as stated above, you're not reinventing the wheel by doing the all the work yourself when you can just drop these controls in, which speeds up development. Secondly these controls are browser aware so will generate JavaScript specific to the type of browser the user is using, thirdly should the user have a browser that doesn't support JavaScript or has it deactivated no errors will be thrown, and more importantly these controls build the server side validation for you as well, so the should the user bypass client side validation the form will still be validated on the server and refused if it fails validation; and again you haven't had to write a single line of code to do that.
Well I hope that helps, any questions just let me know.
Just realised I didn't add a RegularExpressionValidator to validator the web address the user enters, but there are many online you can find if you need it. Also I'm not sure how to get rid of the smileys that have appeared in the code above so you'll need to change them back to proper code obviously.