Query SharePoint Libraries using CAML query and Powershell

$web = Get-SPWeb $siteUrl
$list = $web.Lists[$listName]

1) Query items in list

if($list -ne $null)
{

$caml = '<OrderBy><FieldRef Name="ID" Ascending="True" /></OrderBy><Where><And> <Geq> <FieldRef Name="ID" /><Value Type="Number">{0}</Value> </Geq><Leq><FieldRef Name="ID" /><Value Type="Number">{1}</Value></Leq> </And> </Where> ' -f $startValue,$endValue

$myQuery = new-object Microsoft.SharePoint.SPQuery
$myQuery.Query = $caml

$filteredItems = $list.GetItems($myQuery)

$filteredItems | ForEach-Object {

      #Assign meta data to variables
      $variableOne = $_["MetaDataOne_InternalName"]
}

}

2) Remove specific items from list

if($list -ne $null)
{

$caml='<Where> <Or> <Or> <Or> <Eq> <FieldRef Name="Title" /><Value Type="Text">{0}</Value> </Eq> <Eq> <FieldRef Name="Title" /><Value Type="Text">{1}</Value> </Eq> </Or> <Eq> <FieldRef Name="Title" /><Value Type="Text">{2}</Value> </Eq> </Or> <Eq> <FieldRef Name="Title" /><Value Type="Text">{3}</Value> </Eq> </Or> </Where> ' -f $itemOne, $itemTwo, $itemThree, $itemFour

$query=new-object Microsoft.SharePoint.SPQuery
$query.Query=$caml
$col=$list.GetItems($query)

Write-Host 'Number of items removed: ' $col.Count

$col | % {$list.GetItemById($_.Id).Delete()}

}

$web.Dispose()

for more info about CAML query syntax visit here