JavaScript (ES6), 303 315
Principalement basé sur cette réponse
Modifier 1 
- Suite au commentaire OP, ignorant la casse et forçant tout en minuscules.
- Correction des arguments, maintenant juste un seul argument de chaîne qui est divisé
Remarque: à l'aide de chaînes de modèle, il y a 3 sauts de ligne dans le code qui sont significatifs et inclus dans le nombre d'octets
l=>(l=l.toLowerCase().split`
`).shift(r=l[1].length*4).split` `.map(v=>[2,-2,r,-r,r+2,-r-2,r-2,2-r].map((d,k)=>o.map((t,p)=>[...v].some((c,i)=>z[i?(z[i=t+d/2]=z[i]>' '?'X':'-|\\/'[k>>1],t+=d):t=p]!=c,z=[...o])?0:o=z)),o=[...l.map(s=>' '.repeat(r/2-1)+`
${[...s].join` `}
`).join``.slice(r/2)])&&o.join``
Expliqué (obsolète)
// Note a pattern : in golfed code (but not in the following explanation),
//                  simple operations that have to done before calling .map or .every
//                  are inserted as parameter 2,3,etc... to the same function
//                  as each parameter is evaluated before calling a function
// 
F=( l, // word list as a space separated string
    o, // character grid as a newline separated string - each row is the same length
    // default parameters used as local variables
    r = 4 * o.search`\n` // offset from a line to next nonblank line in resulting output
  )=>(
    w = ' ', // shortcut for blank
    // given the input string in o, build the result as a single dimension array filled with blanks
    // between characters and runs of blank chars betweem each row 
    // .map used as a shorter .forEach
    z = w, // init z to a single blank
    [...o].map( c=> // for each char of o execute the following
                c > w // check if c is a letter (>' ') or a newline
                 ? z+=w+c // if c is a letter, add ' '+c to z
                 : ( // if c is a newline add chars to array o
                     z = z.slice(2), // remove the first 2 char of z ('  ' or '\n ')
                     z = [...z], // convert to array
                     o.push(...z, // push one by one the chars of z
                            c, // then c (a newline)
                            ...z.fill(w), // the same number of char as z, but all blanks
                            z = c // a newline again, meanwhile reset z
                           )
                   )
            , o=[] // o is reset to an empty array just in the map call 
                   // reusing o just to avoid another global variable (no real need in fact)
    ), // end of .map call 
    l.split` `.map( // split l into words and exec the following for each word
      v => [2,-2,r,-r,r+2,-r-2,r-2,2-r].map( // for each scan direction
        (d,k) => // d is the move offset , k is the index 0 to 7
        o.map( // for each char in (including fill blanks and newlines, the scan will fail for them) 
          (t,p) => // t is the first character but NOT USED (var t reused), p is the start position
          (
            z=[...o], // make a copy of o in z
            t = p-d, // current position-d goes in t, it will be incremented before using
            [...v].every( // check the following conditions for every char of word v
            (c,i) => // c: current char of word, i: index used to differentiate the first check when i==0
              (
                // while scanning I already modify the result working copy in z
                i ? // if i != 0 
                  // fill the intermediate position with the right fiil character
                  // based on direction index in k, or X if the position is already full
                  z[i = t+d/2] = z[i] > w ? 'X' : '--||\\\\//'[k]
                : 0, // else do nothing
                // case insensitive comparison, if not a letter parseInt returns NaN that is != from any value
                // this is the condition retured to the .every function
                parseInt(c,36)==parseInt(o[t+=d],36) // meanwhile increment position in T
              )  
            ) ? // check the result of .every
            o = z // if true, update o from the working copy
            : 0 // if false do nothing
          ) // end of o.map operations
        ) // end of o.map function call
      ) // end of direction list map function call
    ) // end of l.split.map function call
    , o.join``
  )
TESTER
console.log=(...x)=>O.textContent+=x.join` `+`\n`;
F=l=>
  (l=l.toLowerCase().split`\n`)
  .shift(r=l[1].length*4).split` `.map(v=>[2,-2,r,-r,r+2,-r-2,r-2,2-r].map((d,k)=>o.map((t,p)=>
    [...v].some((c,i)=>z[i?(z[i=t+d/2]=z[i]>' '?'X':'-|\\/'[k>>1],t+=d):t=p]!=c
    ,z=[...o])?0:o=z)
  ),o=[...l.map(s=>' '.repeat(r/2-1)+`\n${[...s].join` `}\n`).join``.slice(r/2)])
  &&o.join``
  
console.log(F('Atomic chess is cool\nachess\nbtoikm\nbloosi\nnowmlp\nhewiir\nasdfec'))
console.log(F("RANDOM VERTICAL HORIZONTAL WIKIPEDIA Tail WordSearch CODEGOLF UNICORN\nWVERTICALL\nROOAFFLSAB\nACRILIATOA\nNDODKONWDC\nDRKESOODDK\nOEEPZEGLIW\nMSIIHOAERA\nALRKRRIRER\nKODIDEDRCD\nHELWSLEUTH"))
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