For Remove Shipping Methods you need to change its function

This code is working for me in 1.7.0.2 but you can try this for older version also

A) Open Mage/checkout/controllers/Onepagecontroller.php

In this File Go to on function saveBillingAction() 

Check this line in this function and change

From

elseif (isset($data['use_for_shipping']) && $data['use_for_shipping'] == 1) {
$result['goto_section'] = shipping_method;
$result['update_section'] = array(
name => shipping-method,
html => $this->_getShippingMethodsHtml()
);

To

elseif (isset($data['use_for_shipping']) && $data['use_for_shipping'] == 1) {
$result['goto_section'] = payment;
$result['update_section'] = array(
name => payment-method,
html => $this->_getPaymentMethodsHtml()
);

B) Now, In Onepagecontroller.php

Go to on this function public function saveShippingAction()

change this function

From

public function saveShippingAction()
{
if ($this->_expireAjax()) {
return;
}
if ($this->getRequest()->isPost()) {
$data = $this->getRequest()->getPost(shipping, array());
$customerAddressId = $this->getRequest()->getPost(shipping_address_id, false);
$result = $this->getOnepage()->saveShipping($data, $customerAddressId);

if (!isset($result['error'])) {
$result['goto_section'] = shipping_method;
$result['update_section'] = array(
name => shipping-method,
html => $this->_getShippingMethodsHtml()
);
}
$this->getResponse()->setBody(Mage::helper(core)->jsonEncode($result));
}
}

To

public function saveShippingAction()
{
if ($this->_expireAjax()) {
return;
}
if ($this->getRequest()->isPost()) {
$data = $this->getRequest()->getPost(shipping, array());
$customerAddressId = $this->getRequest()->getPost(shipping_address_id, false);
$result = $this->getOnepage()->saveShipping($data, $customerAddressId);

if (!isset($result['error'])) {
$result['goto_section'] = payment;
$result['update_section'] = array(
name => payment-method,
html => $this->_getPaymentMethodsHtml()
);
}
$this->getResponse()->setBody(Mage::helper(core)->jsonEncode($result));
}
}

C) After that Open Code/core/mage/sales/model/service/Quote.php

Find this function  protected function _validate() 

Here comment below code

if ($addressValidation !== true) {
Mage::throwException(
Mage::helper(sales)->__(Please check shipping address information. %s, implode( , $addressValidation))
);
}
$method= $address->getShippingMethod();
$rate = $address->getShippingRateByCode($method);
if (!$this->getQuote()->isVirtual() && (!$method || !$rate)) {
Mage::throwException(Mage::helper(sales)->__(Please specify a shipping method.));
}

D) Open file code/core/mage/checkout/block/onepage/shipping/Method.php

This is hide the Shipping Method tab from the Onepage checkout during Place the order

Find below function

public function isShow()
{
return !$this->getQuote()->isVirtual();
}

Change it with

public function isShow()
{
return false;
}