In fact, you could read Excel file content without any third-party components involved, using SharePoint capabilities only.
The solution demonstrates how to consume SharePoint REST service to read excel data. Another point about this approach, since there is no any dependencies to SharePoint libraries at all, neither server side nor client side assemblies are referenced.
Prerequisite: Excel Services service application has to be configured
Prepare excel data
Assume the following excel file

that contains the following items in the workbook:
Before uploading file into SharePoint library, go to File -> Browse View Options -> choose Items in the Workbook as demonstrated below. Then save file and upload it into SharePoint Documents library.

How to read excel data via Excel Services 2010 REST API
The following example demonstrates how to read excel table content using Excel Services 2010 REST API:
using System;
using System.Net;
namespace SharePoint.Client.Office
{
public class ExcelClient : IDisposable
{
public ExcelClient(Uri webUri, ICredentials credentials)
{
WebUri = webUri;
_client = new WebClient {Credentials = credentials};
}
public string ReadTable(string libraryName,string fileName, string tableName,string formatType)
{
var endpointUrl = string.Format("{0}/_vti_bin/ExcelRest.aspx/{1}/{2}/Model/Tables('{3}')?$format={4}", WebUri,libraryName,fileName, tableName, formatType);
return _client.DownloadString(endpointUrl);
}
public void Dispose()
{
_client.Dispose();
GC.SuppressFinalize(this);
}
public Uri WebUri { get; private set; }
private readonly WebClient _client;
}
}
Usage
The example demonstrates how to read table content using JSON format:
var credentials = new NetworkCredential(userName,password,domain);
var client = new ExcelClient(webUri, credentials);
var tableData = client.ReadTable("Documents","ciscoexpo.xlsx", "CiscoSalesTable","html");
References