one of two parameters mandatory

Hm, I think you have too many parameter sets. Also not sure why you have separate user/password parameters and a PSCredential parameter. You should really just use the PSCredential. But I'll assume you need this for some reason (please consider changing it).

4 parameter sets:

1. ComputerNameCred
2. ComputerNamePlain
3. IpAddressCred
4. IpAddressPlain

function Thing {
    [CmdletBinding(DefaultParameterSetName="ComputerNameCred")]  
    Param
    (
         # computername: Name of the host you want to connect to.
         [Parameter(Mandatory=$true,ParameterSetName="ComputerNameCred", Position=0)]
         [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain", Position=0)]
         [String]$computername,

         # ipAddress: Ip Address of the host you want to connect to.
         [Parameter(Mandatory=$true,ParameterSetName="IpAddressCred", Position=0)]
         [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain", Position=0)]
         [String]$ipAddress,

         # credentials: PowerShell credentials use to connect to the host.
         [Parameter(Mandatory=$true,ParameterSetName="ComputerNameCred")]
         [Parameter(Mandatory=$true,ParameterSetName="IpAddressCred")]
         [PSCredential]$credentials,

         # adminUser: Username to use to connect to the host.
         [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain")]
         [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain")]
         [String]$adminUser,

         # adminPassword: Password to use to connect to the host.
         [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain")]
         [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain")]
         [String]$adminPassword
    )
}

Get-Help Thing # use this to make sure your parameter sets are as they should be.

I also removed [switch] from your IP address parameter; not sure why that was there. You may want to consider using [System.Net.IPAddress] for that parameter instead of [String]. It will still accept strings (they will be cast), but it automatically validates the parameter since the cast will fail if it's not a valid IP.

this is my solution thanks to briantist

[CmdletBinding(DefaultParameterSetName="ComputerName")]  
Param
(
     # computername: Name of the host you want to connect to.
     [Parameter(Mandatory=$true,ParameterSetName="ComputerNameCred", Position=0)]
     [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain", Position=0)]
     [Parameter(Mandatory=$true,ParameterSetName="ComputerName", Position=0)]
     [String]$computername,
     # ipAddress: Ip Address of the host you want to connect to.
     [Parameter(Mandatory=$true,ParameterSetName="IpAddressCred", Position=0)]
     [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain", Position=0)]
     [Parameter(Mandatory=$true,ParameterSetName="IpAddress", Position=0)]
     [String]$ipAddress,

     # credentials: PowerShell credentials use to connect to the host.
     [Parameter(Mandatory=$true,ParameterSetName="ComputerNameCred")]
     [Parameter(Mandatory=$true,ParameterSetName="IpAddressCred")]
     [PSCredential]$credentials,

     # adminUser: Username to use to connect to the host.
     [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain")]
     [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain")]
     [String]$adminUser,

     # adminPassword: Password to use to connect to the host.
     [Parameter(Mandatory=$true,ParameterSetName="IpAddressPlain")]
     [Parameter(Mandatory=$true,ParameterSetName="ComputerNamePlain")]
     [String]$adminPassword,

     # writeLog: Boolean that enables or disables log-writing.
     [Parameter(Mandatory=$false)]
     [Boolean]$writeLog=$true
)