Will a lien filed directly with the county clerk show up in a title search?

A lien filed with the county will certainly show up in a title search.

If there was a strict foreclosure followed by a sheriff's sale, the liens no longer attach to property; however, the liens will remain with whoever they were originally filed against.

Certain liens can be field without judgements.  Mechanics liens are one.  Most others require a court action and a judgement. 

Property purchased at any type of sale like the one you are referring to are usually sold "as is" and subject to the liens on the property. Some liens are against the property itself and some are against a person and filed as against their ownership.  Who is responsible for them will depend on the lien. 

Yes, they will show up on a title search.  It is always a good idea to do one if you are interested in a property you think may be overly encumbered by liens.  A real estate attorney in your area will be able to help you sort out one lien from another.