Python 2, 47 bytes

lambda l:l.sort(key=len)or l[1::2][::-1]+l[::2]

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C# (Visual C# Interactive Compiler), 89 bytes

n=>(n=n.OrderBy(x=>x.Length)).Where((a,b)=>b%2>0).Reverse().Concat(n.Where((a,b)=>b%2<1))

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Jelly, 9 8 bytes

LÞŒœm"-Ẏ

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LÞŒœṚ;¥/

is also 8 bytes.

Thanks to @EriktheOutgolfer and @JonathanAllan for both offering golfs to save a byte.

R, 63 bytes

function(L,b=!seq(L)%%2,o=L[order(nchar(L))])c(rev(o[!b]),o[b])

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Sort by string lengths, then put combine the terms at odd indices (reversed) with terms at even indices.

K (oK), 24 bytes

Solution:

x(<#:'x)(|&~w),&w:2!!#x:

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Explanation:

Generate the 6 4 2 0 1 3 5 sequence, use that to index into the ascending lengths of input, and use that to index into the original array:

x(<#:'x)(|&~w),&w:2!!#x: / the solution
 x: / save input as x
 # / count (#) of x
 ! / range 0 to ...
 2! / modulo 2
 w: / save as w
 & / indices where true
 , / join with
 ( ) / do this together
 ~w / not (~) w
 & / indices where true
 | / reverse
 ( ) / do this together
 #:'x / count (#:) of each (') x
 < / indices to sort ascending
x / index into x

APL+WIN, 31 38 bytes

See Adams comment

⊃n[(⍳⍴n)~a],⌽n[a←2×⍳⌊.5×⍴n←n[⍒∊⍴¨n←⎕]]

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Prompts for a nested vector of strings

PHP, 144 bytes

function($a)usort($a,function($b,$c)return strlen($b)-strlen($c););$e=[];foreach($a as$d)[array_unshift,array_push][++$i%2]($e,$d);return$e;

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Sadly, PHP just doesn't have a lot of syntactic sugar to make this shorter. Submitting it anyway!

Javascript 79 bytes

Takes input as an array of strings, outputs an arrow-sorted array of strings.

f=s=>s.sort((a,b)=>a.length-b.length).reduce((m,x,i)=>i%2?[...m,x]:[x,...m],[])

Explanation

f = s => // take input as an array of strings s
 s.sort((a,b)=>a.length-b.length) // sort input by string length
 .reduce( // reduce
 (m,x,i)=>i%2?[...m,x]:[x,...m], // if index is even, stick string x at the end of the memo
 // array, else at the beginning
 [] // memo initialized to empty array
 )

PowerShell, 66 bytes

1..($a=$args|sort l*).count|?$_%2|%$a[-$_];$x=,$a[-++$_]+$x;$x

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Takes input via splatting, which manifests on TIO as separate command-line arguments. sorts on the length, stores that into $a, and constructs a range from 1 up to the count of input strings. We then pull out only the odd ones ?$_%2 and feed those into a loop |%.... Each iteration, we put the "last", then the "third from last", and so on onto the pipeline with $a[-$_]. Separately, we also accumulate into $x the "second from last", "fourth from last", etc. Out of the loop and the pipeline is flushed (so those elements are output) and then we output $x. In both instances, the default output gives us newlines between items automatically.

Javascript 95 Bytes

s=>s.sort((x,y)=>x.length-y.length).reduce((a,e,i)=>i%2?a.push(e):a.unshift(e);return a;,[]);