Please find in the below code which enables to perform the date validation for any of the supplied format or based on user locale to validate start/from and end/to dates. There could be some better approaches but have come up with this. Have tested it for the formats like: MM/dd/yyyy, dd/MM/yyyy, yyyy-MM-dd, yyyy.MM.dd, yyyy/MM/dd and dd-MM-yyyy. 
Note supplied date format and date string go hand in hand.
<script type="text/javascript">
function validate(format) {
    if(isAfterCurrentDate(document.getElementById('start').value, format)) {
        alert('Date is after the current date.');
    } else {
        alert('Date is not after the current date.');
    }
    if(isBeforeCurrentDate(document.getElementById('start').value, format)) {
        alert('Date is before current date.');
    } else {
        alert('Date is not before current date.');
    }
    if(isCurrentDate(document.getElementById('start').value, format)) {
        alert('Date is current date.');
    } else {
        alert('Date is not a current date.');
    }
    if (isBefore(document.getElementById('start').value, document.getElementById('end').value, format)) {
        alert('Start/Effective Date cannot be greater than End/Expiration Date');
    } else {
        alert('Valid dates...');
    }
    if (isAfter(document.getElementById('start').value, document.getElementById('end').value, format)) {
        alert('End/Expiration Date cannot be less than Start/Effective Date');
    } else {
        alert('Valid dates...');
    }
    if (isEquals(document.getElementById('start').value, document.getElementById('end').value, format)) {
        alert('Dates are equals...');
    } else {
        alert('Dates are not equals...');
    }
    if (isDate(document.getElementById('start').value, format)) {
        alert('Is valid date...');
    } else {
        alert('Is invalid date...');
    }
}
/**
 * This method gets the year index from the supplied format
 */
function getYearIndex(format) {
    var tokens = splitDateFormat(format);
    if (tokens[0] === 'YYYY'
            || tokens[0] === 'yyyy') {
        return 0;
    } else if (tokens[1]=== 'YYYY'
            || tokens[1] === 'yyyy') {
        return 1;
    } else if (tokens[2] === 'YYYY'
            || tokens[2] === 'yyyy') {
        return 2;
    }
    // Returning the default value as -1
    return -1;
}
/**
 * This method returns the year string located at the supplied index
 */
function getYear(date, index) {
    var tokens = splitDateFormat(date);
    return tokens[index];
}
/**
 * This method gets the month index from the supplied format
 */
function getMonthIndex(format) {
    var tokens = splitDateFormat(format);
    if (tokens[0] === 'MM'
            || tokens[0] === 'mm') {
        return 0;
    } else if (tokens[1] === 'MM'
            || tokens[1] === 'mm') {
        return 1;
    } else if (tokens[2] === 'MM'
            || tokens[2] === 'mm') {
        return 2;
    }
    // Returning the default value as -1
    return -1;
}
/**
 * This method returns the month string located at the supplied index
 */
function getMonth(date, index) {
    var tokens = splitDateFormat(date);
    return tokens[index];
}
/**
 * This method gets the date index from the supplied format
 */
function getDateIndex(format) {
    var tokens = splitDateFormat(format);
    if (tokens[0] === 'DD'
            || tokens[0] === 'dd') {
        return 0;
    } else if (tokens[1] === 'DD'
            || tokens[1] === 'dd') {
        return 1;
    } else if (tokens[2] === 'DD'
            || tokens[2] === 'dd') {
        return 2;
    }
    // Returning the default value as -1
    return -1;
}
/**
 * This method returns the date string located at the supplied index
 */
function getDate(date, index) {
    var tokens = splitDateFormat(date);
    return tokens[index];
}
/**
 * This method returns true if date1 is before date2 else return false
 */
function isBefore(date1, date2, format) {
    // Validating if date1 date is greater than the date2 date
    if (new Date(getYear(date1, getYearIndex(format)), 
            getMonth(date1, getMonthIndex(format)) - 1, 
            getDate(date1, getDateIndex(format))).getTime()
        > new Date(getYear(date2, getYearIndex(format)), 
            getMonth(date2, getMonthIndex(format)) - 1, 
            getDate(date2, getDateIndex(format))).getTime()) {
        return true;
    } 
    return false;                
}
/**
 * This method returns true if date1 is after date2 else return false
 */
function isAfter(date1, date2, format) {
    // Validating if date2 date is less than the date1 date
    if (new Date(getYear(date2, getYearIndex(format)), 
            getMonth(date2, getMonthIndex(format)) - 1, 
            getDate(date2, getDateIndex(format))).getTime()
        < new Date(getYear(date1, getYearIndex(format)), 
            getMonth(date1, getMonthIndex(format)) - 1, 
            getDate(date1, getDateIndex(format))).getTime()
        ) {
        return true;
    } 
    return false;                
}
/**
 * This method returns true if date1 is equals to date2 else return false
 */
function isEquals(date1, date2, format) {
    // Validating if date1 date is equals to the date2 date
    if (new Date(getYear(date1, getYearIndex(format)), 
            getMonth(date1, getMonthIndex(format)) - 1, 
            getDate(date1, getDateIndex(format))).getTime()
        === new Date(getYear(date2, getYearIndex(format)), 
            getMonth(date2, getMonthIndex(format)) - 1, 
            getDate(date2, getDateIndex(format))).getTime()) {
        return true;
    } 
    return false;
}
/**
 * This method validates and returns true if the supplied date is 
 * equals to the current date.
 */
function isCurrentDate(date, format) {
    // Validating if the supplied date is the current date
    if (new Date(getYear(date, getYearIndex(format)), 
            getMonth(date, getMonthIndex(format)) - 1, 
            getDate(date, getDateIndex(format))).getTime()
        === new Date(new Date().getFullYear(), 
                new Date().getMonth(), 
                new Date().getDate()).getTime()) {
        return true;
    } 
    return false;                
}
/**
 * This method validates and returns true if the supplied date value 
 * is before the current date.
 */
function isBeforeCurrentDate(date, format) {
    // Validating if the supplied date is before the current date
    if (new Date(getYear(date, getYearIndex(format)), 
            getMonth(date, getMonthIndex(format)) - 1, 
            getDate(date, getDateIndex(format))).getTime()
        < new Date(new Date().getFullYear(), 
                new Date().getMonth(), 
                new Date().getDate()).getTime()) {
        return true;
    } 
    return false;                
}
/**
 * This method validates and returns true if the supplied date value 
 * is after the current date.
 */
function isAfterCurrentDate(date, format) {
    // Validating if the supplied date is before the current date
    if (new Date(getYear(date, getYearIndex(format)), 
            getMonth(date, getMonthIndex(format)) - 1, 
            getDate(date, getDateIndex(format))).getTime()
        > new Date(new Date().getFullYear(),
                new Date().getMonth(), 
                new Date().getDate()).getTime()) {
        return true;
    } 
    return false;                
}
/**
 * This method splits the supplied date OR format based 
 * on non alpha numeric characters in the supplied string.
 */
function splitDateFormat(dateFormat) {
    // Spliting the supplied string based on non characters
    return dateFormat.split(/\W/);
}
/*
 * This method validates if the supplied value is a valid date.
 */
function isDate(date, format) {                
    // Validating if the supplied date string is valid and not a NaN (Not a Number)
    if (!isNaN(new Date(getYear(date, getYearIndex(format)), 
            getMonth(date, getMonthIndex(format)) - 1, 
            getDate(date, getDateIndex(format))))) {                    
        return true;
    } 
    return false;                                      
}
Below is the HTML snippet
    <input type="text" name="start" id="start" size="10" value="05/31/2016" />
<br/> 
<input type="text" name="end" id="end" size="10" value="04/28/2016" />
<br/>
<input type="button" value="Submit" onclick="javascript:validate('MM/dd/yyyy');" />