So here we are looking at 2 onChange client scripts.
1. When Asset changes

var gaCaseEnt = new GlideAjax('global.EntitlementValidation');
gaCaseEnt.addParam('sysparm_name', 'checkEntitlement');
gaCaseEnt.addParam('sysparm_assetName', g_form.getValue('asset'));
gaCaseEnt.getXML(mycallback);

function mycallback(response) {
var answer = response.responseXML.documentElement.getAttribute("answer");
if (answer == 400) {
getMessage("No active contract entitlement is associated with the asset", function(msg) {
alert(msg);
});

}else if(answer=="Start date should not be in future"){
	getMessage("YOUR CUSTOM MESSAGE", function(msg) {
alert(msg);
});
}
	else if(answer=="End date should not be in the past"){
		getMessage("YOUR CUSTOM MESSAGE", function(msg) {
alert(msg);
});}
	else{
		g_form.setValue('asset',answer);
	}

}

2. When Category changes

var gaCaseEnt = new GlideAjax('global.EntitlementValidation');
gaCaseEnt.addParam('sysparm_name', 'checkEntitlement');
gaCaseEnt.addParam('sysparm_assetName', g_form.getValue('asset'));
gaCaseEnt.addParam('sysparm_assetCategory',g_form.getValue('category'));
gaCaseEnt.getXML(mycallback);

function mycallback(response) {
var answer = response.responseXML.documentElement.getAttribute("answer");
if (answer == 400) {
getMessage("No active contract entitlement is associated with the asset", function(msg) {
alert(msg);
});

}else if(answer=="Start date should not be in future"){
	getMessage("YOUR CUSTOM MESSAGE", function(msg) {
alert(msg);
});
}
	else if(answer=="End date should not be in the past"){
		getMessage("YOUR CUSTOM MESSAGE", function(msg) {
alert(msg);
});}
	else{
		g_form.setValue('asset',answer);
	}

}

The script include can be adjusted slightly.

var EntitlementValidation = Class.create();
EntitlementValidation.prototype = Object.extendsObject(AbstractAjaxProcessor, {
checkEntitlement: function() {
var assets = this.getParameter('sysparm_assetName');
if(this.getParameter('sysparm_assetCategory'))
var category= this.getParameter('sysparm_assetCategory');
var type;
if(category=='Hardware')
type= gs.getProperty('<Name of your property>'); //or you can mention the static choice value
else if(category=='Software')
type=gs.getProperty('<Name of your property>'); //or you can mention the static choice value

var serviceEnt = new GlideRecord('service_entitlement');
serviceEnt.addQuery('asset', assets);
serviceEnt.addActiveQuery();
if(type)
serviceEnt.addQuery('u_type', type);//query for the exact type
serviceEnt.orderByDesc('sys_updated_on'); //to get the latest updated record
serviceEnt.setLimit(1);
serviceEnt.query();
if (!serviceEnt.next()) {
return 400;
}
else{
var start= serviceEnt.start_date;
var end= serviceEnt.end_date;
var now= new GlideDate();

if ((start>=now) || (end<=now))
return "No Active Entitlements."
else 
return serviceEnt.getUniqueValue();
}

},

type: 'EntitlementValidation'
});

 
Then it should work. You can test and further adjust based on requirement.

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Best Regards